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

Question 743185: How do I solve:
(5/9)^x=8^(1-x)
Found 2 solutions by lwsshak3, tommyt3rd:
Answer by lwsshak3(11628) (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) (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?).

First we rewrite so that out exponents are now products and we use the fact that

to simplify our equation and we get:

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