Answer
7.61
Work Step by Step
Using the rules of logarithms, we find:
$$\ln \left(4\cdot \:1.171^x\right)=\ln \left(7\cdot \:1.088^x\right) \\ \ln \left(4\right)+\ln \left(1.171^x\right)=\ln \left(7\right)+\ln \left(1.088^x\right) \\ x=\frac{\ln \left(\frac{7}{4}\right)}{\ln \left(\frac{1.171}{1.088}\right)} \\ x=7.61$$