If $l o g_{3} x = a$ , find the value of $81^{a - 1}$ in terms of x.

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Solution

Now,
$l o g_{3} x = a \Rightarrow x = 3^{a}$

Now,

$81^{a - 1}$ $= 81^{a} \times 81^{- 1} = \frac{81^{a}}{81} = \frac{(3^{4})^{a}}{81} = \frac{(3^{a})^{4}}{81} = \frac{x^{4}}{81}$

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