Question

In this exercise, we will establish a formula for the logarithm of a sum. Let ???????? = log(xx + yy), where xx, yy > 0.

Answer 1

Answer:

Assumed that "?????????" means L. And you meant log(x+y)

Let's demonstrate it.

Step-by-step explanation:

$L=\log(x)+\log(1+\frac{y}{x} )\\Let\\\\10^{L}=10^{\log(x)+\log(1+\frac{y}{x} } ) \\\\10^{L}=10^{\log(x)}\times10^{\log(1+\frac{y}{x} })\\10^{L}=x(1+\frac{y}{x})=x+y\\Let\\\log(10^{L})=\log(x+y)\\\\L=\log(x+y)$