Answer
$x = 4$
Work Step by Step
$5(2)^{x} - 4 = 76$
$5(2)^{x} = 80$
$(2)^{x} = 16$
$\log (2)^{x} = \log 16$
$x \log 2 = \log 16$
$x = \frac{\log 16}{\log 2}$
$x = \frac{\log_{10} 2^{4}}{\log_{10} 2^{1}}$
$x = \frac{4}{1}$
$x = 4$
Check:
$5(2)^{4} - 4 \overset{?}{=} 76$
$5(16)- 4 \overset{?}{=} 76$
$80 - 4 \overset{?}{=} 76$
$76 = 76$
