SOLUTION: Can you please help me?!? I have problems with this equation. Can you do it step by step?? I want to see what I'm doing wrong. Please & thank you! log<base 5> (x^2 - 100) = 1 +

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Can you please help me?!? I have problems with this equation. Can you do it step by step?? I want to see what I'm doing wrong. Please & thank you! log<base 5> (x^2 - 100) = 1 +       Log On


   

Question 250999: Can you please help me?!? I have problems with this equation. Can you do it step by step?? I want to see what I'm doing wrong. Please & thank you!
log (x^2 - 100) = 1 + log (x + 10)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
log(x^2 - 100) = 1 + log(x + 10)
:
We can factor the expression on the left (it's the "difference of squares")
log ((x-10)(x+10)) = 1 + log (x + 10)
:
Subtract log(x+10) from both sides
log ((x-10)(x+10)) - log (x + 10) = 1
:
Can be written as, (subtraction of logs means divide)
log%28%28%28%28x-10%29%28x%2B10%29%29%2F%28x%2B10%29%29%29 = 1
:
Cancel (x+10) and you have:
log(x-10) = 1
:
exponent equiv of logs
10^1 = x - 10
10 = x - 10
10 + 10 = x
x = 20
:
Check this solution on your calc, enter
log(20^2 - 100) - log(20 + 10) results = 1