If 5^(3x^2 log10 2) = 2^((x+1/2)log10 25), then the value of x is: -Maths 9th

If 5^(3x^2 log10 2) = 2^((x+1/2)log10 25), then the value of x is: -Maths 9th
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(d) \(-rac{1}{3}\)\(5^{{3x^2}log_{10}2}\) = 2\(\big(x+rac{1}{2}\big)\)log10 25⇒ \(5^{{3x^2}log_{10}2}\) = 2\(\big(rac{2x+1}{2}\big)\) x log10 5  = 2(2x+1)log10 5⇒ \(5^{{3x^2}log_{10}2}\) = 2(2x+1)log2 5. log10 2           (using loga x = logb x . loga b)⇒ \(5^{{3x^2}log_{10}2}\) = [\(2^{log_25^{(2x+1)}}\)] log10 2⇒ \(\big(5^{{3x^2}}\big)\)log10 2 = (52x+1)log10 2               [Using aloga x = x]⇒ 3x2 = 2x + 1 ⇒ 3x2 – 2x – 1 = 0 ⇒ (x – 1) (3x + 1) = 0⇒ x = 1, \(-rac{1}{3}\)
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