Chapter 12 - Section 12.3 - Exponential Functions - Exercise Set - Page 861: 27

$x=-\dfrac{2}{3}$

$\dfrac{1}{4}=2^{3x}$ Rewrite $4$ as $2^{2}$: $\dfrac{1}{2^{2}}=2^{3x}$ Take $2^{2}$ to the numerator by changing the sign of its exponent: $2^{-2}=2^{3x}$ If $2^{-2}=2^{3x}$, then $3x=-2$ $3x=-2$ Solve for $x$: $x=-\dfrac{2}{3}$