Optimization problem whose objective function is a sum of exponentials

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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?