Answer
$x \approx 0.567$
Work Step by Step
$5(4)^{3x+2} - 830 = 14.5$
$5(4)^{3x+2} = 14.5 + 830$
$5(4)^{3x+2} = 844.5$
$(4)^{3x+2} = 168.9$
$3x + 2 = \log_4 168.9$
$3x = \log_4 168.9 - 2$
$x = \frac{(\log_4 168.9) - 2}{3}$
$x = \frac{(\frac{\log 168.9}{\log 4}) - 2}{3}$
by GDC / calculator
$x = 0.566670...$
$x \approx 0.567$
