Logarithm Subject of Formula

Question

$G_{dB}(f) = −10 \log_{10}(1 +\left(\frac f{f_3}\right)^2N)$. I will like to make $N$ the subject of the formula. Any lead on how to achieve this will be appreciated.

Answer 1

To solve for $N$ in terms of other variables, consider dividing by $-10$ by both sides, and convert the equation to exponential form: $$10^{-\frac{G_{dB}(f)}{10}}=1+\left(\frac f{f_3}\right)^2 N$$ Perhaps you can solve for $N$ algebraically from here?