How do I solve for $\delta$ in this question

Question

$316.45 = 100e^{\delta(10)} + 100e^{\delta(5)}$

I don't know why I can't do this. I thought of using $\ln$ but I don't think $\ln(A+B) = \ln(A) + \ln(B)$ or does it?

Answer 1

Hint: Let $x = e^{5\delta}$. Notice that $e^{10\delta} = (e^{5\delta})^2$. Then we have

$$316.45 = 100x^2 + 100x$$

Solve as usual for $x$, and retrieve $\delta$ afterwards.

Answer 2

we have $\ln(ab)=\ln(a)+\ln(b)$ and your equation is simplified $3.1645=e^{\delta(10)}+e^{\delta(5)}$