Answer
$log_37\approx1.771$
Work Step by Step
Step 1. Multiply $u=3^{x}$ on both sides, we have $u^2-14-5u=0 \longrightarrow (u+2)(u-7)=0\longrightarrow u=-2,7$
Step 2. For $u=-2$, we have $3^x=-2 \longrightarrow $ no real solution.
Step 3. For $u=7$, we have $3^x=7 \longrightarrow x=log_37\approx1.771$
