Solve for logarithmic equation. Log on one side.

Question

How do I solve for $k$ in the following equation?

$$\log _{10}4 = 2k$$

I expect that the solution will be pretty simple, yet I can't seem to figure it out.

Answer 1

If $2k=\log_{10} 4,$ then $k=\dfrac{\log_{10}4}2$.

Furthermore, $\log_{10}4=\log_{10}2^2=2\log_{10}2$, so $k=\log_{10}2$.

Answer 2

Obviously, $k=\dfrac{1}{2}\log_{10} 4$, but we can further simplify it.

By using the identity $b\log a=\log a^b$, $k=\log_{10} 4^\frac{1}{2}=\boxed{\log_{10} 2}$