Find the value of x, if log2 (5.2^x + 1), log4(2^(1–x) + 1) and 1 are in A.P. -Maths 9th

Find the value of x, if log2 (5.2^x + 1), log4(2^(1–x) + 1) and 1 are in A.P. -Maths 9th
by

1 Answer

Answer :

(b) 1 – log25 Given, log2 (5.2x + 1), log4 (21– x + 1), 1 are in A.P. ⇒ log2 (5.2x + 1) + 1 = 2 log4 (21 – x + 1) ⇒ log2 (5.2x + 1) + log22 = 2 log22 (21-x + 1)⇒ log2 (5.2x + 1).2 = 2 x \(rac12\)log2 (21-x + 1)\(\big(\because\, ext{log}_{a^n}x=rac{1}{n} ext{log}_ax\big)\)⇒ log2 (10.2x + 2) = log2 (21-x + 1)⇒ 10.2x + 2 = 21 – x + 1 ⇒ 10.2x + 2 = \(rac{2}{2^x}\) + 1Let 2x = a, then10. a + 2 = \(rac{2}{a}\) + 1 ⇒ 10a + 1 = \(rac{2}{a}\) ⇒ 10 a2 + a – 2 = 0⇒ (5 a – 2) (2a + 1) = 0 ⇒ a = \(rac{2}{5}\) ⇒ 2x = \(rac{2}{5}\)\(\big(\because\,2^x>0, ext{reject}\,a=-rac{1}{2}\big)\)⇒ log 2x = log \(rac{2}{5}\)⇒ x log2 2 = log2 2 – log2 5 ⇒ \(x\) = 1 – log2 5.
by

Related questions

The number of meaningful solutions of log4(x – 1) = log2 (x – 3) is -Maths 9th

Description : The number of meaningful solutions of log4(x – 1) = log2 (x – 3) is -Maths 9th

Last Answer : (b) 1log4(x - 1) = log2(x - 3) ⇒ log22 (x − 1) = log2(x - 3)⇒ \(rac{1}{2}\) log2 (x-1) = log2 (x- 3) ⇒ log2 (x-1) = 2 log2 (x- 3)\(\big[\)Using logam (bn) = \(rac{n}{m} ... x = 2 or 5 Neglecting x = 2 as log2(x - 3) is defined when x > 2.⇒ There is only one meaningful solution of the given equation.

The number of solution of log4 (x – 1) = log2 (x – 3) is : -Maths 9th

Description : The number of solution of log4 (x – 1) = log2 (x – 3) is : -Maths 9th

Last Answer : answer:

If log2 [log7(x^2 – x + 37)] = 1, then what could be the value of x ? -Maths 9th

Description : If log2 [log7(x^2 – x + 37)] = 1, then what could be the value of x ? -Maths 9th

Last Answer : (c) 4log2 [log7(x2 – x + 37)] = 1 ⇒ log7(x2 – x + 37) = 21 = 2 ⇒ x2 – x + 37 = 72 = 49 ⇒ x2 – x – 12 = 0 Now solve for x.

Solve for x : log10 [log2 (log39)] = x -Maths 9th

Description : Solve for x : log10 [log2 (log39)] = x -Maths 9th

Last Answer : answer:

The number log2 7 is : -Maths 9th

Description : The number log2 7 is : -Maths 9th

Last Answer : (c) an irrational numberLet us assume log27 be a rational number. Then, log27 = \(rac{p}{q}\), where p,q ∈ I and q ≠ 0 ⇒ \(2^{rac{p}{q}}\) = 7 ⇒ 2p = 7q This is not true as 2 is even and 7 is odd.∴ Hence our assumption that log27 is a rational number is wrong. ∴ log27 is an irrational number.

If Log2 x - 5 Log x + 6 = 0, then what would the value(s) of x be?

Description : If Log2 x - 5 Log x + 6 = 0, then what would the value(s) of x be?

Last Answer : Answer: x = e2 or e3.

2 . If the mean of the following distribution is 6 . Find the value of p ? x 2 4 6 10 P + 5 f 3 2 3 1 2 -Maths 9th

Description : 2 . If the mean of the following distribution is 6 . Find the value of p ? x 2 4 6 10 P + 5 f 3 2 3 1 2 -Maths 9th

Last Answer : Here's ur answer...

2 . If the mean of the following distribution is 6 . Find the value of p ? x 2 4 6 10 P + 5 f 3 2 3 1 2 -Maths 9th

Description : 2 . If the mean of the following distribution is 6 . Find the value of p ? x 2 4 6 10 P + 5 f 3 2 3 1 2 -Maths 9th

Last Answer : Here's ur answer...

If the polynomial x^6 + px^5 + qx^4 – x^2 – x – 3 is divisible by x^4 – 1, then the value of p^2 + q^2 is : -Maths 9th

Description : If the polynomial x^6 + px^5 + qx^4 – x^2 – x – 3 is divisible by x^4 – 1, then the value of p^2 + q^2 is : -Maths 9th

Last Answer : The divisor is x4−1=(x−1)(x+1)(x2+1) By factor theorem, f(1)=f(−1)=0 Thus, 1+p+q−1−1−3=0 and 1+q−1−3=p−1 i.e., p+q=4 and p−q=−2 Adding the two, 2p=2 i.e. p=1 and ∴ q=3. ∴ p2+q2=1+9=10

If log32, log3 (2^x – 5) and log^3 (2^x – 7/2) are in A.P., then what is the value of x ? -Maths 9th

Description : If log32, log3 (2^x – 5) and log^3 (2^x – 7/2) are in A.P., then what is the value of x ? -Maths 9th

Last Answer : answer:

For what value of k,(x+1) is a factor of p(x) - kx(square) - x - 4 ? -Maths 9th

Description : For what value of k,(x+1) is a factor of p(x) - kx(square) - x - 4 ? -Maths 9th

Last Answer : Solution :-

Find the value of k if (x-2)is a factor of polynomial p(x) = 2x(cube) - 6x(square) + 5x + k. -Maths 9th

Description : Find the value of k if (x-2)is a factor of polynomial p(x) = 2x(cube) - 6x(square) + 5x + k. -Maths 9th

Last Answer : Solution :-

Find the value of the polynomial p(x) = x^3-3x^2-2x+6 at x = underroot 2 -Maths 9th

Description : Find the value of the polynomial p(x) = x^3-3x^2-2x+6 at x = underroot 2 -Maths 9th

Last Answer : In this chapter, we shall proceed with recalling some of the constructions already learnt in the earlier classes and deal with some more. Here in this section, we will construct some of these ... be done? 2. Always explain the construction. Write the sequence of steps that are actually taken.

Two students A and B solve an equation of the form x^2 + px + q = 0. A starts with a wrong value of p and obtains the roots as 2 and 6. -Maths 9th

Description : Two students A and B solve an equation of the form x^2 + px + q = 0. A starts with a wrong value of p and obtains the roots as 2 and 6. -Maths 9th

Last Answer : Let αα and ββ be the roots of the quadratic equation x2+px+q=0x2+px+q=0 Given that, A starts with a wrong value of p and obtains the roots as 2 and 6. But this time q is correct. i.e., a product of roots ... 1 Now, from Eqs. (ii) and (iii), we get α=−3 and β=−4α=−3 and β=−4 which are correct roots.

Let p and q be the roots of the quadratic equation x^2 – (a – 2)x – a – 1 = 0. What is the minimum possible value of p^2 + q^2 ? -Maths 9th

Description : Let p and q be the roots of the quadratic equation x^2 – (a – 2)x – a – 1 = 0. What is the minimum possible value of p^2 + q^2 ? -Maths 9th

Last Answer : answer:

For what value of p is the coefficient of x^2 in the product (2x – 1) (x – k) (px + 1) equal to 0 and the constant term equal to 2 ? -Maths 9th

Description : For what value of p is the coefficient of x^2 in the product (2x – 1) (x – k) (px + 1) equal to 0 and the constant term equal to 2 ? -Maths 9th

Last Answer : answer:

If the expressions (px^3 + 3x^2 – 3) and (2x^3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ? -Maths 9th

Description : If the expressions (px^3 + 3x^2 – 3) and (2x^3 – 5x + p) when divided by (x – 4) leave the same remainder, then what is the value of p ? -Maths 9th

Last Answer : Given that the following polynomials leave the same remainder when divided by (x - 4) : We are to find the value of a. Remainder theorem: When (x - b) divides a polynomial p(x), then the remainder is p(b). So, from (i) and (ii), we get Thus, the required value of a is 1.

If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th

Description : If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. -Maths 9th

Last Answer : p(x) = (k2 – 14) x2 – 2x – 12 Here a = k2 – 14, b = -2, c = -12 Sum of the zeroes, (α + β) = 1 …[Given] ⇒ − = 1 ⇒ −(−2)2−14 = 1 ⇒ k2 – 14 = 2 ⇒ k2 = 16 ⇒ k = ±4

log2 (x + 1) = How do I get x from Equation 5?

Description : How to calculate the logarithmic equation below? log2 (x + 1) = 5

Last Answer : We take the fifth power of 2, it's 32, it's x + 1, so x = 31

The value of 1.999… in the form of p/q, where p and q are integers and -Maths 9th

Description : The value of 1.999… in the form of p/q, where p and q are integers and -Maths 9th

Last Answer : Value of 1.999 is given below .

The value of 1.999… in the form of p/q, where p and q are integers and -Maths 9th

Description : The value of 1.999… in the form of p/q, where p and q are integers and -Maths 9th

Last Answer : Value of 1.999 is given below .

if (1.-2) is a solution of the equation 2x-y=p,then find the value of p. -Maths 9th

Description : if (1.-2) is a solution of the equation 2x-y=p,then find the value of p. -Maths 9th

Last Answer : x = 1 y = -2 2x-y = p Therefore, p = 2(1)-(-2) = 2 + 2 = 4

if (1.-2) is a solution of the equation 2x-y=p,then find the value of p. -Maths 9th

Description : if (1.-2) is a solution of the equation 2x-y=p,then find the value of p. -Maths 9th

Last Answer : 2x-y=p put x-1,y=-2 =2(1)-(-2)=p p=4

If p = 100r – t, find the value of p when r = 0.25 and t = 10. -Maths 9th

Description : If p = 100r – t, find the value of p when r = 0.25 and t = 10. -Maths 9th

Last Answer : Solution :-

For what value of p the point (p, 2) lies on the line 3x + y = 11? -Maths 9th

Description : For what value of p the point (p, 2) lies on the line 3x + y = 11? -Maths 9th

Last Answer : Solution :-

If the mean of the following data is 20.2, find the value of p: -Maths 9th

Description : If the mean of the following data is 20.2, find the value of p: -Maths 9th

Last Answer : x̅ = ∑fx/∑f ∴ 20.2 = 610 + 20p/30 + p ⇒ 20.2(30 + p) = 610 + 20p ⇒ 606 + 20.2p = 610 + 20p ⇒ 20.2p - 20p = 610 - 606 ⇒ 0.2p = 4 ⇒ p = 4/0.2 = 40/2 ⇒ p = 20

If a, b, c be the p^th, q^th, r^th terms of a GP, then the value of (q – r) log a + (r – p) -Maths 9th

Description : If a, b, c be the p^th, q^th, r^th terms of a GP, then the value of (q – r) log a + (r – p) -Maths 9th

Last Answer : (a) 0Let h be the first term and k be the common ratio of a GP, then a = hkp - 1, b = hkq - 1, c = hkr - 1∴ (q - r) log a + (r - p) log b + (p - q) log c = log [hkp -1]q - r + log [hkq -1]r - p + log[hkr -1]p - ... r + r - p + p - q) (kp - 1)q - r (kq -1)r - p (kr -1)p - q = log(ho ko) = log 1 = 0.

If pqr = 1, the value of (1)/([1+p+q^-1]) + (1)/([1+q+r^-1])+ (1)/([1+r+p^-1]) will be equal to : -Maths 9th

Description : If pqr = 1, the value of (1)/([1+p+q^-1]) + (1)/([1+q+r^-1])+ (1)/([1+r+p^-1]) will be equal to : -Maths 9th

Last Answer : answer:

A and B are two mutually exclusive and exhaustive events with P(B) = 3P(A). What is the value of P (bar(B)) ? -Maths 9th

Description : A and B are two mutually exclusive and exhaustive events with P(B) = 3P(A). What is the value of P (bar(B)) ? -Maths 9th

Last Answer : (c) 43 : 34Given, odds against A = 8 : 3⇒ P(not A) = \(rac{8}{8+3}\) = \(rac{8}{11}\) ⇒ P(A happens) = \(rac{3}{11}\)Odds against B = 5 : 2⇒ P(not B) = \(rac{5}{5+2}\) = \(rac{5}{7}\) ⇒ P(B happens ... {43}{77}\)odds against C = \(rac{P(not\,c)}{P(c)}\) = \(rac{rac{43}{77}}{rac{34}{77}}\) = 43 : 34.

Determine the ratio in which the point P(m, 6) divides the join of A(– 4, 3) and B(2, 8). Also find the value of m. -Maths 9th

Description : Determine the ratio in which the point P(m, 6) divides the join of A(– 4, 3) and B(2, 8). Also find the value of m. -Maths 9th

Last Answer : (b) 1 : 2Any point on the x-axis is (a, 0).Let the point (a, 0) divide the join of A(2, -3) and B(5, 6) in the ratio k : 1. Then the co-ordinates of the point of division are \(\bigg(rac{5k+2}{k+1},rac{6k-3}{k+1}\ ... 6k - 3 = 0 ⇒ k = \(rac{1}{2}\)Required ratio is k : 1 ⇒ \(rac{1}{2}\) : 1 = 1 : 2.

Zero of the polynomial p(x)=2x+5 is -Maths 9th

Description : Zero of the polynomial p(x)=2x+5 is -Maths 9th

Last Answer : (b) Given, p(x) = 2x+5 For zero of the polynomial, put p(x) = 0 ∴ 2x + 5 = 0 ⇒ -5/2 Hence, zero of the polynomial p(x) is -5/2.

If the perpendicular distance of a point P from the X-axis is 5 units and the foot of the perpendicular lies on the negative direction of X-axis, then the point P has -Maths 9th

Description : If the perpendicular distance of a point P from the X-axis is 5 units and the foot of the perpendicular lies on the negative direction of X-axis, then the point P has -Maths 9th

Last Answer : (d) We know that, the perpendicular distance of a point from the X-axis gives y-coordinate of that point. Here, foot of perpendicular lies on the negative direction of X-axis, so perpendicular distance can be measure in II quadrant or III quadrant. Hence, the point P has y-coordinate = 5 or -5.

If P (5,1), Q (8, 0), R(0, 4), S(0, 5) and O(0, 0) are plotted on the graph paper, then the points on the X-axis is/are -Maths 9th

Description : If P (5,1), Q (8, 0), R(0, 4), S(0, 5) and O(0, 0) are plotted on the graph paper, then the points on the X-axis is/are -Maths 9th

Last Answer : (d) We know that, a point lies on X-axis, if its y-coordinate is zero. So, on plotting the given points on graph paper, we get Q and O lie on the X-axis.

Which of the points P(0, 3), Q(l, 0), R(0, – 1), S(-5, 0) and T(1, 2) do not lie on the X-axis ? -Maths 9th

Description : Which of the points P(0, 3), Q(l, 0), R(0, – 1), S(-5, 0) and T(1, 2) do not lie on the X-axis ? -Maths 9th

Last Answer : (c) We know that, if a point is of the form (x, 0)i.e., its y-coordinate is zero, then it will lie on X-axis otherwise not. Here, y-coordinates of points P(0, 3), R (0, -1) and T (1,2) are not zero, so these points do not lie on the X-axis.

Zero of the polynomial p(x)=2x+5 is -Maths 9th

Description : Zero of the polynomial p(x)=2x+5 is -Maths 9th

Last Answer : (b) Given, p(x) = 2x+5 For zero of the polynomial, put p(x) = 0 ∴ 2x + 5 = 0 ⇒ -5/2 Hence, zero of the polynomial p(x) is -5/2.

If the perpendicular distance of a point P from the X-axis is 5 units and the foot of the perpendicular lies on the negative direction of X-axis, then the point P has -Maths 9th

Description : If the perpendicular distance of a point P from the X-axis is 5 units and the foot of the perpendicular lies on the negative direction of X-axis, then the point P has -Maths 9th

Last Answer : (d) We know that, the perpendicular distance of a point from the X-axis gives y-coordinate of that point. Here, foot of perpendicular lies on the negative direction of X-axis, so perpendicular distance can be measure in II quadrant or III quadrant. Hence, the point P has y-coordinate = 5 or -5.

If P (5,1), Q (8, 0), R(0, 4), S(0, 5) and O(0, 0) are plotted on the graph paper, then the points on the X-axis is/are -Maths 9th

Description : If P (5,1), Q (8, 0), R(0, 4), S(0, 5) and O(0, 0) are plotted on the graph paper, then the points on the X-axis is/are -Maths 9th

Last Answer : (d) We know that, a point lies on X-axis, if its y-coordinate is zero. So, on plotting the given points on graph paper, we get Q and O lie on the X-axis.

Which of the points P(0, 3), Q(l, 0), R(0, – 1), S(-5, 0) and T(1, 2) do not lie on the X-axis ? -Maths 9th

Description : Which of the points P(0, 3), Q(l, 0), R(0, – 1), S(-5, 0) and T(1, 2) do not lie on the X-axis ? -Maths 9th

Last Answer : (c) We know that, if a point is of the form (x, 0)i.e., its y-coordinate is zero, then it will lie on X-axis otherwise not. Here, y-coordinates of points P(0, 3), R (0, -1) and T (1,2) are not zero, so these points do not lie on the X-axis.

If an integer P is chosen at random in the interval 0 ≤ p ≤ 5, the probability that the roots of the equation x^2 + px -Maths 9th

Description : If an integer P is chosen at random in the interval 0 ≤ p ≤ 5, the probability that the roots of the equation x^2 + px -Maths 9th

Last Answer : answer:

If m is a power of 2, the number of select lines required for an m-input mux is: a. m b. 2^m c. log2 (m) d. 2*m

Description : If m is a power of 2, the number of select lines required for an m-input mux is: a. m b. 2^m c. log2 (m) d. 2*m

Last Answer : c. log2 (m)

A full binary tree with n leaves contains (A) n nodes (B) log2 n nodes (C) 2n –1 nodes (D) 2n nodes

Description : A full binary tree with n leaves contains (A) n nodes (B) log2 n nodes (C) 2n –1 nodes (D) 2n nodes

Last Answer : (C) 2n –1 nodes 

p(x)=x3+3x2+3x+1, g(x) = x+2 -Maths 9th

Description : p(x)=x3+3x2+3x+1, g(x) = x+2 -Maths 9th

Last Answer : p(x) = x3+3x2+3x+1, g(x) = x+2 g(x) = 0 ⇒ x+2 = 0 ⇒ x = −2 ∴ Zero of g(x) is -2. Now, p(−2) = (−2)3+3(−2)2+3(−2)+1 = −8+12−6+1 = −1 ≠ 0 ∴By factor theorem, g(x) is not a factor of p(x

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th

Description : Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x3+x2–2x–1, g(x) = x+1 -Maths 9th

Last Answer : Solution: p(x) = 2x3+x2–2x–1, g(x) = x+1 g(x) = 0 ⇒ x+1 = 0 ⇒ x = −1 ∴Zero of g(x) is -1. Now, p(−1) = 2(−1)3+(−1)2–2(−1)–1 = −2+1+2−1 = 0 ∴By factor theorem, g(x) is a factor of p(x

Determine the remainder when polynomial p(x) is divided by x - 2 . -Maths 9th

Description : Determine the remainder when polynomial p(x) is divided by x - 2 . -Maths 9th

Last Answer : p(x) = x4 - 3x2 + 2x - 5 According to remainder theorem, the required remainder will be = p(2) p(x) = x4 - 3x2 + 2x - 5 ∴ p(2) = 24 - 3(2)2 + 2(2) - 5 =16 - 12 + 4 - 5 = 3

If p (x) = x + 3, then p(x)+ p (- x) is equal to -Maths 9th

Description : If p (x) = x + 3, then p(x)+ p (- x) is equal to -Maths 9th

Last Answer : (d) Given p(x) = x+3, put x = -x in the given equation, we get p(-x) = -x+3 Now, p(x)+ p(-x) = x+ 3+ (-x)+ 3=6

If p (x) = x2 – 4x + 3, then evaluate p(2) – p (-1) + p (1/2). -Maths 9th

Description : If p (x) = x2 – 4x + 3, then evaluate p(2) – p (-1) + p (1/2). -Maths 9th

Last Answer : Solution of this question

Find the zeroes of the polynomial p(x)= (x – 2)2 – (x+ 2)2. -Maths 9th

Description : Find the zeroes of the polynomial p(x)= (x – 2)2 – (x+ 2)2. -Maths 9th

Last Answer : Given, polynomial is p(x) = (x – 2)2 – (x+ 2)2 For zeroes of polynomial, put p(x) = 0 (x – 2)2 – (x+ 2)2 = 0 (x-2 + x+2)(x-2-x-2) = 0 [using identity, a2-b2 =(a-b)(a + b)] ⇒ (2x)(-4) = 0

Check whether p(x) is a multiple of g(x) or not -Maths 9th

Description : Check whether p(x) is a multiple of g(x) or not -Maths 9th

Last Answer : p(x) is a multiple of g(x) or not

By remainder theorem, find the remainder when p(x) is divided by g(x) -Maths 9th

Description : By remainder theorem, find the remainder when p(x) is divided by g(x) -Maths 9th

Last Answer : Find the remainder when p(x) is divided by g(x)

The polynomial p{x = x4 -2x3 + 3x2 -ax+3a-7 when divided by x+1 leaves the remainder 19. -Maths 9th

Description : The polynomial p{x = x4 -2x3 + 3x2 -ax+3a-7 when divided by x+1 leaves the remainder 19. -Maths 9th

Last Answer : p(x) is divided by x+ 2 =