Answer
1.224
Work Step by Step
$5(0.10)^x=4(0.12)^x$
$\ln[5(0.10)^x]=\ln [4(0.12)^x]$
$\ln5 + x\ln0.10 = \ln 4 +x\ln0.12$
$x\ln 0.10-x\ln 0.12=\ln 5 - \ln 4$
$x(\ln0.10-\ln0.12)=\ln 5- \ln 4$
$x(\ln\frac{0.10}{0.12})=\ln\frac{5}{4}$
$x \approx 1.224$
