SOLUTION: (1/3) to the power of x = 6 to the 1-x power I have tried to solve this but I keep getting different answers. What are the correct steps and solution? Thank you

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: (1/3) to the power of x = 6 to the 1-x power I have tried to solve this but I keep getting different answers. What are the correct steps and solution? Thank you      Log On


   

Question 433757: (1/3) to the power of x = 6 to the 1-x power
I have tried to solve this but I keep getting different answers. What are the correct steps and solution?
Thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
(1/3) to the power of x = 6 to the 1-x power
%281%2F3%29%5Ex = 6%5E%281-x%29
Using natural logs
ln%28%281%2F3%29%5Ex%29 = ln%286%5E%281-x%29%29
the log equiv of exponents
x*ln%281%2F3%29 = (1-x)*ln%286%29
Find the nat logs of both
-.10986x = 1.79176(1-x)
-.10986x = 1.79176 - 1.79176x
1.79176x - 1.0986 = 1.79176
.693x = 1.79176
x = 1.79176%2F.693
x = 2.585
;
:
Check this with a calc
enter (1/3)^2.585, results .05843
enter 6^(1-2.585), results .05843; confirms our solution of x=2.585