Question 597972
{{{ 5^(x^2-3x )= 625 }}}
Note that {{{ 625 = 5^4 }}}
Let {{{ y = x^2 - 3x }}}
{{{ 5^y = 5^4 }}}
Take the log to base {{{5}}} of both sides
{{{ log( 5, 5^y ) = y }}}
{{{ log( 5, 5^4 ) = 4 }}}
{{{ y = 4 }}}
{{{ x^2 - 3x = 4 }}}
{{{ x^2 -3x - 4 = 0 }}}
{{{ ( x - 4 )*( x + 1 ) = 0 }}}
{{{ x = 4 }}}
{{{ x = -1 }}}
Both these answers work in original equation