# Question #ab197

Aug 17, 2016

See the Explanation given below.

#### Explanation:

$x = \log \frac{\frac{1}{9}}{\log} y$ : Upto this, it is OK. Now, we proceed further as

shown below :

$\therefore \log y = \log \frac{\frac{1}{9}}{x} = \frac{1}{x} \log \left(\frac{1}{9}\right) = \log {\left(\frac{1}{9}\right)}^{\frac{1}{x}}$.

Since, $\log$ function is $1 - 1$, we have,

$y = {\left(\frac{1}{9}\right)}^{\frac{1}{x}}$.

Otherwise, we can proceed further from this step$: {y}^{x} = \frac{1}{9}$

$\therefore {\left({y}^{x}\right)}^{\frac{1}{x}} = {\left(\frac{1}{9}\right)}^{\frac{1}{x}}$

$\therefore {y}^{x \cdot \frac{1}{x}} = {\left(\frac{1}{9}\right)}^{\frac{1}{x}}$, i.e.,

$y = {\left(\frac{1}{9}\right)}^{\frac{1}{x}}$, as we have derived before!

Enjoy Maths.!