Question 1130719


{{{10^(4log(x)) - 7(10^(2log(x)) )+ 10 = 0 }}}


since {{{10^(4log(x))=10^(2log(x))*10^(2log(x))}}}, we have


{{{10^(2log(x))*10^(2log(x)) - 7(10^(2log(x)) )+ 10 = 0 }}}


{{{10^(2log(x))*10^(2log(x)) - 2(10^(2log(x)) )- 5(10^(2log(x)) )+ 10 = 0 }}}


{{{(10^(2log(x))*10^(2log(x)) - 2(10^(2log(x)) ))- (5(10^(2log(x)) )- 10) = 0 }}}


{{{10^(2log(x))(10^(2log(x)) - 2)-5 (10^(2log(x)) - 2) = 0 }}}


{{{(10^(2log(x))-5 )(10^(2log(x)) - 2) = 0 }}}

solutions:

{{{10^(2log(x))-5 =0}}}

{{{10^(2log(x)) =5}}}

{{{log(10^(2log(x))) =log(5)}}}

{{{(2log(x))log(10) =log(5)}}}

{{{(2log(x))*1 =log(5)}}}

{{{log(x^2) =log(5)}}}

{{{x^2=5}}}

{{{highlight(x=sqrt(5)) }}} or {{{highlight(x=-sqrt(5))}}}


{{{(10^(2log(x)) - 2) = 0 }}}

{{{10^(2log(x))  = 2}}}

{{{log(10^(2log(x)))  = log(2)}}}

{{{2log(x)*log(10)=log(2)}}}

{{{log(x^2)*1=log(2)}}}

{{{x^2=2}}}

{{{highlight(x=sqrt(2))}}} or {{{highlight(x=-sqrt(2))}}}