Chapter 7 - Exponential and Logarithmic Functions - 7-5 Exponential and Logarithmic Equations - Practice and Problem-Solving Exercises - Page 473: 8

$x=\frac{3}{2}=1.5$

Notice that $27=3^3$ so the given equation is equivalent to: $3^{2x}=3^3$ Using the rule $a^m=a^n\longrightarrow m=n$ gives: $2x=3$ $x=\frac{3}{2}=1.5$ Check: $3^{2*1.5}=27$ $3^{3}=27$ Thus, we have confirmed that the answer is correct.