Question

find the value of log 256/81 to the base 4/3

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{log\,_{\frac{4}{3}}\left(\dfrac{256}{81}\right)}$

$\underline{\textbf{To find:}}$

$\textsf{The value of}\;\mathsf{log\,_{\frac{4}{3}}\left(\dfrac{256}{81}\right)}$

$\underline{\textbf{Solution:}}$

$\mathsf{Let\;\;x=log\,_{\frac{4}{3}}\left(\dfrac{256}{81}\right)}$

$\textsf{This can be written as}$

$\mathsf{\left(\dfrac{4}{3}\right)^x=\dfrac{256}{81}}$

$\mathsf{\left(\dfrac{4}{3}\right)^x=\dfrac{4^4}{3^4}}$

$\mathsf{\left(\dfrac{4}{3}\right)^x=\left(\dfrac{4}{3}\right)^4}$

$\textsf{Equating powers on bothsides, we get}$

$\mathsf{x=4}$

$\implies\boxed{\bf\;log\,_{\frac{4}{3}}\left(\dfrac{256}{81}\right)=4}$

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