SOLUTION: How do you solve equations with the following type of exponents? 2^2n-1=8^n+7 Thanks for your help.

Algebra ->  Exponents -> SOLUTION: How do you solve equations with the following type of exponents? 2^2n-1=8^n+7 Thanks for your help.      Log On


   

Question 33063: How do you solve equations with the following type of exponents?
2^2n-1=8^n+7
Thanks for your help.
Answer by sarah_adam(201) About Me  (Show Source):
You can put this solution on YOUR website!
2^2n-1=8^n+7
take logs on both sides
(2n-1)log 2 = (n+7) log 8
(2n-1)log 2 = (n+7) log(2^3) {8=2^3}
(2n-1)log 2 = 3*(n+7)log 2 ( according to log a^b = blog a)
cancelling log 2 on both sides
(2n-1)= 3*(n+7)
2n - 1 = 3n +21
n = -22