Question 433757
(1/3) to the power of x = 6 to the 1-x power 
{{{(1/3)^x}}} = {{{6^(1-x)}}}
Using natural logs
{{{ln((1/3)^x)}}} = {{{ln(6^(1-x))}}}
the log equiv of exponents
x*{{{ln(1/3)}}} = (1-x)*{{{ln(6)}}}
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/.693}}}
x = 2.585
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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