SOLUTION: We are trying to solve the following problem: {{{2^x=5^(x+1)}}} I understand that it is necessary to get the base the same, but I don't understand how to get 5 to a base of 2.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: We are trying to solve the following problem: {{{2^x=5^(x+1)}}} I understand that it is necessary to get the base the same, but I don't understand how to get 5 to a base of 2.       Log On


   

Question 223206: We are trying to solve the following problem:
2%5Ex=5%5E%28x%2B1%29
I understand that it is necessary to get the base the same, but I don't understand how to get 5 to a base of 2.
Thank you, in advance!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2%5Ex=5%5E%28x%2B1%29
Take the log of both sides
log%282%5Ex%29+=+log%285%5E%28x%2B1%29%29
x%2Alog%282%29+=+%28x%2B1%29%2Alog%285%29
log(2) and log(5) are just constants.
x*log(2) = x*log(5) + log(5)
x*log(2) - x*log(5) = log(5)
x*(log(2) - log(5)) = log(5)
x = log(5)/log(0.4)
x = ~ -1.75647