# How do you solve (4/3)^x=27/64?

May 23, 2015

${\left(\frac{4}{3}\right)}^{x} = \frac{27}{64}$

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

upon taking the reciprocal of the second term the sign of the exponent will reverse from positive to negative.

${\left(\frac{4}{3}\right)}^{x} = {\left(\frac{4}{3}\right)}^{-} 3$

now we can equate the exponents for the expression:
$x = - 3$ is the solution.