Find the value of $\log^{\frac{8}{27}}_{\frac{2}{3}}$.

Given:

\log^{\frac{8}{27}}_{\frac{2}{3}}
To do:

We have to find the value of \log^{\frac{8}{27}}_{\frac{2}{3}}.
Solution:

We know that,

$\log^{b^m}_{a}=m\log^{b}_{a}$
$\log^{a}_{a}=1$ 

Therefore,

$ \begin{array}{l}
\log^{\frac{8}{27}}_{\frac{2}{3}} =\log^{\left(\frac{2}{3}\right)^{3}}_{\frac{2}{3}}\\
\\
=3\log^{\frac{2}{3}}_{\frac{2}{3}}\\
\\
=3\times 1\\
\\
=3
\end{array}$

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Updated on: 10-Oct-2022

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