Answer
$x \approx 3.98$
Work Step by Step
$\log (8x^{5}) - \log (2x) = 3$
$\log \frac{8x^{5}}{2x} = 3$
$\log \frac{8x^{4}}{2} = 3$
$\log 4x^{4} = 3$
$10^{3} = 4x^{4}$
$1000 = 4x^{4}$
$250 = x^{4}$
$x = 250^{\frac{1}{4}}$
$x$ must be greater than zero, so we take only the positive root.
$x = 3.976...$
$x \approx 3.98$
Check:
$\log (8x^{5}) - \log (2x) \overset{?}{=} 3$
$\log (8(3.976...)^{5}) - \log (2(3.976...)) \overset{?}{=} 3$
$\log (8(994.088...)) - \log (7.952) \overset{?}{=} 3$
$\log (7952.707...) - \log (7.952) \overset{?}{=} 3$
$3=3$
