Alg9.4.12

Find the value of x if $\log_x(4)=\frac{-1}{3}\,$

Let $\log_a(m)=k\,$ which can be expressed as $m=a^k\,$

Applying this to the given equation,it looks like,

$4=x^{\frac{-1}{3}}\,$

Cubing both sides,we get

$4^3=(x^{\frac{-1}{3}})^{3}\,$

$64=x^{-1}\,$

This can be expressed as

$64=\frac{1}{x}\,$

Hence

$x=\frac{1}{64}\,$