find the value of $k$ in the term $2^{-k} = 1/n$

Question

What is the value of $k$ if I have the following equation: $2^{-k} = \frac1n$?

$$2^{-k} = \frac 1 n \implies n = 2^k \implies \log_{2} n = k$$

Is my solution correct?

Answer 1

Yes your solution is correct

$$2^{-k} = \frac 1 n \implies n = 2^k \implies \log_{2} n = k$$

Answer 2

$$k=\frac{\log\left(n\right)+2i\pi c_1}{\log\left(2\right)}$$ for any integer $c_1$, where $\log$ is the natural logarithm and $i$ is the imaginary unit.