Question 990682
Use the substitution:
{{{ 1 = log( 4,4 ) }}}
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{{{ log( 4,x^2 ) - log( 4,x-1 ) = log( 4,4 ) }}}
{{{ log( 4, x^2/(x-1) ) = log( 4,4 ) }}}
{{{ x^2/( x-1 ) = 4 }}}
{{{ x^2 = 4x - 4 }}}
{{{ x^2 - 4x + 4 = 0 }}}
{{{ ( x - 2 )^2 = 0 }}}
{{{ x = 2 }}}
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check:
{{{ log( 4,x^2 ) - log( 4,x-1 ) = 1 }}}
{{{ log( 4,2^2 ) - log( 4,2-1 ) = 1 }}}
{{{ log( 4,4 ) - log( 4,1 ) = 1
{{{ 1 - 0 = 1 }}}
OK