SOLUTION: Find the exact solution, using common logarithms: 5^x+125(5^-x)=30

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find the exact solution, using common logarithms: 5^x+125(5^-x)=30      Log On


   

Question 712630: Find the exact solution, using common logarithms:
5^x+125(5^-x)=30
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Common logarithms not necessary, pointless. See how this solution works:

5%5Ex%2B125%285%5E%28-x%29%29=30, as given.
5%5Ex%2B125%2F%285%5Ex%29-30=0
Multiply both sides by 5^x.
%285%5Ex%295%5Ex%2B125%2A%285%5Ex%29%285%5E%28-x%29%29-30%2A5%5Ex=0%2A5%5Ex
5%5E%282x%29-30%2A5%5Ex%2B125=0, which is factorable.
highlight%28%285%5Ex-5%29%285%5Ex-25%29=0%29

Taking 5%5Ex-5=0, 5^x=5, x=1.

Taking 5%5Ex-25=0, 5^x=25, 5^x=5^2, x=2.

Answer: highlight%28x=1%29 or highlight%28x=2%29.