Question about basic exponential/logarithm properties

Question

Solve for $k$: $$e^{k/2}=a$$

Solution: $$e^{2k}=a$$

$$ k/2 = \mathbf{ln}a$$

$$ k=2\mathbf{ln}a$$

$$= \mathbf{ln}a^2$$

My question is: why does $2\mathbf{ln}a = \mathbf{ln}a^2$? Why can you transfer the $2$ to be an exponent of $a$?

Answer 1

Because logarithms map multiplication to addition:

$\ln ab= \ln a+\ln b$

So in particular:

$\ln a^2= \ln a+\ln a=2\ln a$