Question 1163250
<font color=black size=3>
{{{log(2,(x)) + log(3,(81)) = 1}}}


{{{log(2,(x)) + log((81))/log((3)) = 1}}} Change of base property. Only change {{{log(3,(81))}}}


{{{log(2,(x)) + log((3^4))/log((3)) = 1}}} Rewrite 81 as 3^4


{{{log(2,(x)) + 4*log((3))/log((3)) = 1}}} Use the rule that log(x^y) = y*log(x).


{{{log(2,(x)) + 4*highlight(log((3)))/highlight(log((3))) = 1}}}


{{{log(2,(x)) + 4*cross(log((3)))/cross(log((3))) = 1}}}


{{{log(2,(x)) + 4*1 = 1}}} 


{{{log(2,(x)) + 4 = 1}}} 


{{{log(2,(x)) = 1-4}}} Subtracting 4 from both sides

 
{{{log(2,(x)) = -3}}} 


{{{x = 2^(-3)}}} Convert from log form to exponent form

 
{{{x = 1/(2^3)}}}

 
{{{x = 1/8}}} <font color=red>is the final answer</font>. This is equivalent to 0.125 in decimal form. 
</font>