Answer
$x=1$
Work Step by Step
Given Expression
$5(1.2)^{3x-2}+1=7$
Subtract 1 from both sides.
$5(1.2)^{3x-2}=6$
Divide both sides by 5.
$1.2^{3x-2}=\frac{6}{5}$
Take log of both sides.
$\log1.2^{3x-2}=\log\frac{6}{5}$
Power Rule of logarithms.
$(3x-2)\log1.2=\log\frac{6}{5}$
Solve for $x$.
$x=((\frac{\log\frac{6}{5}}{\log1.2})+2)\div3$
$x=1$