SOLUTION: Solve 2(5^(x-2))= 9 -5^(x-2). (Hint: First solve for 5^(x-2) Then take the log (or ln) of both sides.) Please help. I do not understand this. Thanks in advance.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve 2(5^(x-2))= 9 -5^(x-2). (Hint: First solve for 5^(x-2) Then take the log (or ln) of both sides.) Please help. I do not understand this. Thanks in advance.      Log On


   

Question 429093: Solve 2(5^(x-2))= 9 -5^(x-2). (Hint: First solve for 5^(x-2) Then take the log (or ln) of both sides.) Please help. I do not understand this. Thanks in advance.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
First, I will presume you know the definition and basic properties of logarithms.

We can definitely solve for 5%5E%28x-2%29 by letting a+=+5%5E%28x-2%29. Our equation becomes 2a+=+9+-+a --> 3a+=+9 --> a+=+5%5E%28x-2%29+=+3. Taking the log base 5 of both sides, we get

log%285%2C5%5E%28x-2%29%29+=+log%285%2C3%29
x-2+=+log%285%2C3%29
x+=+log%285%2C3%29+%2B+2.