Answer
$$6.518$$
Work Step by Step
Using the rules of logarithms, we find:
$$\ln \left(5\right)+\ln \left(1.15^t\right)=\ln \left(8\right)+\ln \left(1.07^t\right) \\ t=\frac{\ln \left(\frac{8}{5}\right)}{\ln \left(\frac{1.15}{1.07}\right)} \\ t=6.518$$
