3−2=91Taking log on both sides−2log3=log91log391=−2.....(since logbloga=logba)

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Given 3^{x} = {1}{9} then x=?

Question

Given $3^{x} = \frac{1}{9}$ then $x = ?$

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Sophia Discussed

Given

3^{x} = \frac{1}{9}

then

x = ?

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Text solutionVerified

3^{- 2} = \frac{1}{9}

Taking log on both sides

- 2 l o g 3 = l o g \frac{1}{9}

l o g_{3} \frac{1}{9} = - 2

.....(since

\frac{l o g a}{l o g b} = l o g_{b} a

)

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