Question

Can someone please help me

Answer 1

Where's the trick. Just wade through it!

\(ln(x-8) - ln(x+7) = ln(x-10) - ln(x+8)\)

Why don't we tackle that last part, first.

x - 8 > 0 ==> x > 8
x + 7 > 0 ==> x > -7
x - 10 > 0 ==> x > 10
x + 8 > 0 ==> x > -8

Okay, then, we have narrowed the Domain down to x > 10. ANY result less than 10, or equal to 10, will be discarded.

Logarithm Rules

\(ln\left(\dfrac{x-8}{x+7}\right) = ln\left(\dfrac{x-10}{x+8}\right)\)

Now what?