Evaluate $\log 64$ using the change of base formula?

Question

Is that even possible? I mean, there is no base.

Answer 1

Usually, $\log$ means $\log_e = \ln$ or $\log_{10}$. Either way, there isn't a neat answer to the question. The most you can do is write $\ln 64 = 6\ln 2$ and $\log_{10}64 = 6 \log_{10}2$, using that $2^6=64$. Now the problem boils down to knowing the values of $\ln 2$ and $\log_{10}2$. These values can be approximated numerically using calculus, for example.