Question

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

.
a. Show log(x) + log (1 + y/x)=L
State as a property of logarithms after showing this is a true statement

Answer 1

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

Let's demonstrate it.

Explanation:

`L=\log(x)+\log(1+(y)/(x) )\\Let\\\\10^(L)=10^{\log(x)+\log(1+(y)/(x) } ) \\\\10^(L)=10^(\log(x))*10^{\log(1+(y)/(x) })\\10^(L)=x(1+(y)/(x))=x+y\\Let\\\log(10^(L))=\log(x+y)\\\\L=\log(x+y)\\\\`