In How to find the value of an unknown exponent?, user504882 provided an answer which inspired me to develop the following formula for solving exponential problems of the form $a^{k_1x + k_0} = b$ for $x$:
$$ x = \log_a[(\frac{b}{a^{k_0}})^{\frac{1}{k_1}}]. $$
On inspection, I see this can be simplified to
$$ x = \frac{\log_a(b) - k_0}{k_1} ,$$
following well-known laws of logarithms. Does this formula have a name? Can it be generalised, say to exponents with rational quadratics or complex polynomials?
(If this sort of question is more approprate for the Math Exchange, feel free to migrate it.)