I have an optimization problem whose objective function I am trying to minimize is
$$0.3^x + 0.4^y$$
Unfortunately, this isn't a linear function. I was thinking of converting it to a linear function by taking the logarithm of each term, i.e., converting it to
$$\log(0.3^x)+\log(0.4^y)$$
The reason I can't take the logarithm of the entire function is because this results in a non-linear function.
Is this a valid way to solve the optimization problem, or will applying a logarithm to each term skew the result? My intuition is that I have to apply an operator to the entire equation, not individual terms, meaning this won't work. Is there a way to solve this optimization problem?