SOLUTION: Let f(x)= π^2 and g(x) = e^x. Then solve the following equation and give answer(s) in exact form: f(x-1)-2∙g(2x-1)=0

Algebra ->  Rational-functions -> SOLUTION: Let f(x)= π^2 and g(x) = e^x. Then solve the following equation and give answer(s) in exact form: f(x-1)-2∙g(2x-1)=0      Log On


   

Question 1154521: Let f(x)= π^2 and g(x) = e^x. Then solve the following equation and
give answer(s) in exact form:
f(x-1)-2∙g(2x-1)=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let
f%28x%29=+pi%5E2+-> constant
g%28x%29+=+e%5Ex

Then solve the following equation and give answer(s) in exact form:

f%28x-1%29-2g%282x-1%29=0...........f%28x-1%29=+pi%5E2+,g%282x-1%29+=+e%5E%282x-1%29

pi%5E2-2%28e%5E%282x-1%29%29=0

pi%5E2=2%28e%5E%282x-1%29%29

pi%5E2%2F2=e%5E%282x-1%29...take log of both sides

log%28pi%5E2%2F2%29=log%28e%5E%282x-1%29%29

log%28pi%5E2%2F2%29=%282x-1%29log%28e%29......log%28e%29=1

log%28pi%5E2%29-log%282%29=2x-1

2log%28pi%29-log%282%29%2B1=2x

x=2log%28pi%29%2F2-log%282%29%2F2%2B1%2F2

x=log%28pi%29-log%282%29%2F2%2B1%2F2