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Logarithmic Differentiation

Solve the fol...

Question

Solve the following equation:
${log}_{3} ({log}_{9} x + \frac{1}{2} + 9^{x}) = 2 x$

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Solution

${log}_{9} x + \frac{1}{2} + 9^{x} = 3^{2 x} = 9^{x} {log}_{9} x = - \frac{1}{2} x = 9^{- 1 / 2} x = \frac{1}{3}$

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