Question 1151062
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{{{log(8,x)+log(4,(1/6)) = 1/3}}}<br>
Convert the log base 8 and the log base 4 to logs base 2:<br>
{{{(1/3)log(2,x)+(1/2)log(2,(1/6))= 1/3}}}<br>
Convert the expression on the left to a single log base 2 using rules of logarithms:<br>
{{{log(2,((x^(1/3)*(1/6)^(1/2)))) = 1/3}}}<br>
Convert the logarithmic equation to exponential form:<br>
{{{x^(1/3)*(1/sqrt(6)) = 2^(1/3)}}}<br>
Isolate the term with the variable:<br>
{{{x^(1/3) = 2^(1/3)*sqrt(6)}}}<br>
Cube both sides of the equation:<br>
{{{x = 2*(6*sqrt(6))}}}
{{{x = 12*sqrt(6)}}}<br>