# Thread: sum or differences of logs

1. ## sum or differences of logs

needing help with finding the sum or difference of the function:
log_a x-y overthe square root of x^2-y^2

2. Hello, bastropgarl!

Note sure what you're asking for . . .

needing help with finding the sum or difference of the function:

. . . $\log_a\left(\frac{x-y}{\sqrt{x^2-y^2}}\right)$

We have: . $\log_a\left(\frac{x-y}{\sqrt{(x-y)(x+y)}}\right)$

. . . . . . . . $=\;\log_a\left(\frac{x-y}{(x-y)^{\frac{1}{2}}(x+y)^{\frac{1}{2}}}\right)$

. . . . . . . . $=\;\log_a\left(\frac{(x-y)^{\frac{1}{2}}}{(x+y)^{\frac{1}{2}}}\right)$

. . . . . . . . $=\;\log_a\left(\frac{x-y}{x+y}\right)^{\frac{1}{2}}$

. . . . . . . . $=\;\frac{1}{2}\log_a\left(\frac{x-y}{x+y}\right)$

. . . . . . . . $= \;\frac{1}{2}\bigg[\log_a(x-y) - \log_a(x+y)\bigg]$