Question 1015407
use the substitution:
{{{ 1 = log(4,4) }}}
{{{ log( 4,x ) + log( 4, x-2 ) = log( 4,4 ) }}}
{{{ log( 4, x*( x-2 ) ) = log( 4,4 ) }}}
{{{ x*( x-2 ) = 4 }}}
{{{ x^2 - 2x = 4 }}}
Complete the square
{{{ x^2 - 2x + (-2/2 )^2 = 4 + (-2/2 )^2 }}}
{{{ x^2 - 2x + 1 = 4 + 1 }}}
{{{ ( x - 1 )^2 = 5 }}}
Take the square root of both sides
{{{ x - 1 = sqrt(5) }}}
{{{ x = 1 + sqrt(5) }}}
and also:
{{{ x - 1 = -sqrt(5) }}}
{{{ x = 1 - sqrt(5) }}}
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check:
{{{ x*( x-2 ) = 4 }}}
{{{ ( 1 + sqrt(5) )*( -1 + sqrt(5) ) = 4 }}}
{{{ -1 + 5 = 4 }}}
{{{ 4 = 4 }}}
OK
You can check the other answer