Answer
$m \approx -2.926$
Work Step by Step
$3(4.6)^{2m+7} = 17.3$
$(4.6)^{2m+7} = \frac{17.3}{3}$
$2m + 7 = \log_{4.6} (\frac{17.3}{3})$
$2m = \frac{\log \frac{17.3}{3}}{\log 4.6} - 7$
$m = \frac{\frac{\log \frac{17.3}{3}}{\log 4.6} - 7}{2}$
by GDC / calculator
$m = -2.92594...$
$m \approx -2.926$