How do you solve ${(\frac{4}{3})}^{x} = \frac{27}{64}$ $(4/3)^x=27/64$ ?

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Answer 1 · 2015-05-23T09:38:52

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

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

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

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

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

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