Question 1058225
Convert {{{ 2 }}} to a log to the base 5
{{{ log( 5, 7+x ) + log( 5, 8-x ) - log( 5, 2 ) = 2 }}}
{{{ log( 5, 7+x ) + log( 5, 8-x ) - log( 5, 2 ) = log( 5, 25 ) }}}
{{{ log( 5, ( 7+x )*( 8 - x )/2 ) = log( 5, 25 ) }}}
{{{ ( 7+x )*( 8-x )/2 = 25 }}}
{{{ ( 7+x )*( 8-x ) = 50 }}}
{{{ 56 + 8x - 7x - x^2 = 50 }}}
{{{ -x^2 + x + 6 = 0 }}}
{{{ ( -x + 3 )*( x + 2 ) = 0 }}} ( I  just figured it out )
{{{ x = 3 }}}
{{{ x = -2 }}}
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check:
I'll check {{{ x = -2 }}}
{{{ log( 5, 7+x ) + log( 5, 8-x ) - log( 5, 2 ) = 2 }}}
{{{ log( 5, 7-2 ) + log( 5, 8+2 ) - log( 5, 2 ) = 2 }}}
{{{ log( 5, 5 ) + log( 5, 10 ) - log( 5, 2 ) = 2 }}}
{{{ 1 + log( 5,2 ) + log( 5,5 ) - log( 5,2 ) = 2 }}}
{{{ 1 + 1 = 2 }}}
OK
You can check {{{ x=3 }}}