Question 826046
Express {{{ 1 }}} as a log to
the base {{{ 2}}}
{{{ 1 = log( 2,2 )
{{{ log( 2,(x-2)) + log(2,(x+5)) = 1 }}}
{{{ log( 2,(x-2)) + log(2,(x+5)) = log(2,2) }}}
{{{ log( 2, (x-2)*(x+5) ) = log(2,2) }}}
{{{ (x-2)*(x+5) = 2 }}}
{{{ x^2 + 3x - 10 = 2 }}}
{{{ x^2 + 3x -12 = 0 }}}
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{{{ x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = 3 }}}
{{{ c = -12 }}}
{{{ x = (-3 +- sqrt( 3^2 - 4*1*(-12) )) / (2*1) }}}
{{{ x = (-3 +- sqrt( 9 + 48 )) / 2 }}}
{{{ x = (-3 +- sqrt( 57 )) / 2 }}}
{{{ x = ( -3 + 7.5498 ) / 2 }}}
{{{ x = 4.5498/2 }}}
{{{ x = 2.2749 }}}
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The negative square root can't be used, since that
gives me a log that results in a negative number
( {{{ log( 2,( x-2 )) }}} )
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check:
{{{ log( 2,(x-2)) + log(2,(x+5)) = 1 }}}
{{{ log( 2,(2.2749-2)) + log(2,(2.2749+5)) = 1 }}}
{{{ log( 2,(.2749)) + log(2,(7.2749)) = log( 2,2 ) }}}
{{{ log( 2, 1.9998 ) = log( 2,2 ) }}}
{{{ 1.9998 = 2 }}}
close enough