Answer
$x \approx 0.315$
Work Step by Step
$5 \log (2x) + 4 = 3$
$5\log 2x = 3 - 4$
$5 \log 2x = -1$
$\log 2x = -\frac{1}{5}$
$10^{(-\frac{1}{5})} = 2x$
$x = \frac{10^{(-\frac{1}{5})}}{2}$
$x \approx 0.315$
Check:
$5 \log (2x) + 4 \overset{?}{=} 3$
$5 \log (2(\frac{10^{(-\frac{1}{5})}}{2})) + 4 \overset{?}{=} 3$
$5 \log (10^{(-\frac{1}{5})}) + 4 \overset{?}{=} 3$
$5(-0.2) + 4 \overset{?}{=} 3$
$-1 + 4 \overset{?}{=} 3$
$3 = 3$
