Question 985278
{{{log(x^7)*log(x) - log(x^2) - 5 = 0}}}
{{{7*log(x)*log(x) - 2*log(x) - 5 = 0 }}}
{{{ 7*log(x)^2 - 2 log(x) - 5 = 0}}}
Let {{{ y = log(x) }}}

{{{ 7y^2 - 2y - 5 = 0}}}

Use quadratic formula

{{{y = (-(-2) +- sqrt((-2)^2 - 4*7*(-5)))/(2*7)}}}

{{{y = (2 +- sqrt(4+140))/14}}}

{{{y = (2 +- 12) / 14}}}

{{{ y = -6/14 , 1 }}}

First, deal with {{{y = -6/14}}}

{{{y = -6/14}}}

{{{log(x) = -6/14}}}

{{{x = 10^(-6/14) = .373}}}

Now deal with {{{y = 1}}}

{{{y = 1}}}

{{{log(x) = 1}}}

{{{x = 10^1 = 10}}}

Since {{{.373 < 1}}}, then we only accept {{{highlight(x = 10)}}}