SOLUTION: 2^(x + 4) = 5^(x - 3) round to the 4th decimal place. I've tried switching them over to log form and solving out but it seems it's always wrong.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 2^(x + 4) = 5^(x - 3) round to the 4th decimal place. I've tried switching them over to log form and solving out but it seems it's always wrong.      Log On


   

Question 631545: 2^(x + 4) = 5^(x - 3) round to the 4th decimal place. I've tried switching them over to log form and solving out but it seems it's always wrong.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%28x+%2B+4%29 = 5%5E%28x+-+3%29

log%28%282%5E%28x+%2B+4%29%29%29 = log%28%285%5E%28x+-+3%29%29%29

(x+4)log(2) = (x-3)log(5)

Let log(2) = A and log(5) = B

(x+4)A = (x-3)B

A(x+4) = B(x-3)

Ax+4A = Bx-3B

Ax-Bx = -4A-3B

x(A-B) = -4A-3B

x = %28-4A-3B%29%2F%28A-B%29

x = %28-4log%28%282%29%29-3log%28%285%29%29%29%2F%28log%28%282%29%29-log%28%285%29%29%29

Get your calculator. 

x = 8.295295582 rounds to 8.2953

Edwin