Question

what is the value of x in this logarithmic equation?$\frac{1}{g^{5}} = (g^{ \frac{9}{5}})^{x}$

Answer 1

$\frac{1}{g^5}=(g^{\frac{9}{5}})^x$

This can be re-written as;

$g^{-5}=g^{\frac{9x}{5}}$

we can now equate the powers

$-5\text{ =}\frac{9x}{5}$

Multiply both-side of the equation by 5/9

-5(5/9) = x

-25/9 = x

$x=-2\frac{7}{9}$

or

x= -2.78