SOLUTION: How do I solve: (5/9)^x=8^(1-x)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do I solve: (5/9)^x=8^(1-x)      Log On


   

Question 743185: How do I solve:
(5/9)^x=8^(1-x)
Found 2 solutions by lwsshak3, tommyt3rd:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
How do I solve:
(5/9)^x=8^(1-x)
take log of both sides:
xlog(5/9)=(1-x)log8
-0.2553x=0.9031(1-x)
-0.2553x=0.9031-0.9031x
0.6478x=0.9031
x=0.9031/0.6478
x=1.3941

Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
log functions are inverses of exponential functions. We have two choices. In this case we'll use log base 8 (can you see why?).
%285%2F9%29%5Ex=8%5E%281-x%29
log_base+8%28%285%2F9%29%5Ex%29=log_base+8%28%288%29%5E%281-x%29%29%29
First we rewrite so that out exponents are now products and we use the fact that

log_base+8%28%288%29%29=1
to simplify our equation and we get:
x%2Alog_base+8%285%2F9%29=1-x
x%2Alog_base+8%285%2F9%29%2Bx=1
x%2A%28log_base+8%285%2F9%29%2B1%29=1

x=1%2F%28log_base+8%285%2F9%29%2B1%29