Answer
$x\approx6.5788$
Work Step by Step
Given expression
$1.2(.9)^x=6$
Divide both sides by 1.2.
$(.9)^x=0.5$
Take log of both sides.
$\log(.9)^x=\log0.5$
Use the Power Rule of logarithms.
$x\log0.9=\log0.5$
Solve for $x$.
$x=\frac{\log0.5}{\log0.9}$
$x\approx6.5788$