Answer
7.407
Work Step by Step
$1.5(1.05)^x=2(1.01)^x$
$\ln[1.5(1.05)^x]=\ln [2(1.01)^x]$
$\ln1.5 + x\ln1.05 = \ln 2 +x\ln1.01$
$x\ln1.05-x\ln1.01=\ln 2 - \ln 1.5$
$x(\ln1.05-\ln1.01)=\ln 2 - \ln 1.5$
$x(\ln\frac{1.05}{1.01})=\ln\frac{2}{1.5}$
$x \approx 7.407$