Question 1203185
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To avoid having to type all those log expressions....<br>
Define {{{y=log(x,5)}}}<br>
The given equation is<br>
{{{6log(x,25)=7-log(5,x)}}}<br>
Note {{{log(x,25)=log(x,5^2)=2log(x,5)}}} and {{{log(5,x)=1/log(x,5)}}}<br>
Then the equation is<br>
{{{6(2y)=7-1/y}}}
{{{12y=7-1/y}}}
{{{12y^2=7y-1}}}
{{{12y^2-7y+1=0}}}
{{{(4y-1)(3y-1)=0}}}<br>
The possible solutions are {{{y=1/4}}} and {{{y=1/3}}}.<br>
{{{y=1/4}}} --> {{{log(x,5)=1/4}}} --> {{{x^(1/4)=5}}} --> {{{x=5^4=625}}}<br>
{{{y=1/3}}} --> {{{log(x,5)=1/3}}} --> {{{x^(1/3)=5}}} --> {{{x=5^3=125}}}<br>
ANSWERS: x=125 and x=625<br>