Question 1203185
{{{ 6log(x,25 )= 7 - log(5,x)}}}

{{{ 6log(25 )/log(x)= 7 - log(x)/log(5)}}}

{{{ 6log(25 )/log(x)= (7log(5) - log(x))/log(5)}}}

{{{ 6log(25 )log(5)= log(x)(7log(5) - log(x))}}}

{{{ 6log(5^2 )log(5)= log(x)*7log(5) - log(x)*log(x)}}}

{{{ 6 *2log^2(5)= 7log(x)*log(5) - log^2(x)}}}

{{{ log^2(x)-7log(x)*log(5)+12log^2(5)=0}}}

let {{{ log(x)=u}}}

{{{ u^2-7u*log(5)+12log^2(5)=0}}}

{{{ u=(7log(5)+-sqrt((-7log(5))^2-4*1*12log^2(5)))/(2*1)}}}

{{{ u=(-(-7log(5))+-sqrt(49log^2(5)-48log^2(5)))/2}}}

{{{ u=(7log(5)+-sqrt(log^2(5)))/2}}}

{{{ u=(7log(5)+-log(5))/2}}}


{{{ u=(7log(5)+log(5))/2}}}=>{{{u=6log(5)/2}}}=>{{{u=3log(5)}}}
or
{{{ u=(7log(5)-log(5))/2}}}=>{{{u=8log(5)/2}}}=>{{{u=4log(5)}}}



{{{ log(x)=u}}} , then {{{ log(x)=3log(5)}}} or {{{ log(x)=4log(5)}}}



solutions

{{{ log(x)=3log(5)}}} ....solve for{{{  x}}}

{{{ log(x)=log(5^3)}}}

{{{ x=5^3}}}

{{{ highlight(x=125)}}}


or

{{{ log(x)=4log(5)}}}.....solve for {{{x}}}

{{{ log(x)=log(5^4)}}}

{{{ x=5^4}}}

{{{ highlight(x=625)}}}