Answer
$x \approx 1.166$
Work Step by Step
$3(4.2)^{x} + 7 = 23$
$3(4.2)^{x} = 23 - 7$
$3(4.2)^{x} = 16$
$4.2^{x} = \frac{16}{3}$
$x = \log_{4.2} \frac{16}{3}$
$x = \frac{\log \frac{16}{3}}{\log 4.2}$
$x = 1.16646...$
$x \approx 1.166$
Check:
$3(4.2)^{(1.166...)} + 7 \overset{?}{=} 23$
$16+ 7 \overset{?}{=} 23$
$23 = 23$