Kasey Reese

2022-10-26

Evaluate $\mathrm{log}64$ using the change of base formula?
Is that even possible? I mean, there is no base.

Tirioliwo

Expert

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