Question 437888
Get logs on both sides.
First, express {{{1}}} as a log to the base {{{4}}}
{{{ 1 = log(4,4) }}}
Rewrite the equation:
{{{ log(4,(x^2 - 3x)) = log(4,4) }}}
{{{ x^2 - 3x = 4 }}}
{{{ x^2 - 3x - 4 = 0 }}}
{{{ (x-4)*(x+1) = 0 }}}
{{{ x = 4 }}}
{{{ x = -1 }}}
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check answers:
{{{ log(4,(x^2 - 3x)) = log(4,4) }}}
{{{ log(4,(4^2 - 3*4)) = log(4,4) }}}
{{{ log(4,4) = log(4,4) }}}
and
{{{ log(4,((-1)^2 - 3*(-1))) = log(4,4) }}}
{{{ log(4, (1+3)) = log(4,4) }}}
{{{ log(4,4) = log(4,4) }}}