Question 617078
Use the general rule:
{{{ log(a) + log(b) = log(a*b) }}}
Also, express the right side as a log to base 4
{{{ log(4,2x-7) + log(4,3x-3) = 4 }}}
{{{ log(4, (2x-7)*(3x-3)) = log(4,256) }}}
{{{ (2x-7)*(3x-3) = 256 }}}
{{{ 3*(2x-7)*(x-1) = 256 }}}
{{{ 3*( 2x^2 - 7x - 2x + 7 ) = 256 }}}
{{{ 2x^2 - 9x + 7 = 256/3 }}}
{{{ 2x^2 - 9x - 235/3 }}}
{{{ x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = 2 }}}
{{{ b = -9 }}}
{{{ c = -235/3 }}}
{{{ x = (-(-9) +- sqrt( (-9)^2 - 4*2*(-235/3) )) / (2*2) }}} 
{{{ x = ( 9 +- sqrt( 81 + 1880/3) )) / 4 }}} 
{{{ x = ( 9 +- sqrt( 243/3 + 1880/3) )) / 4 }}} 
{{{ x = ( 9 +- sqrt( 2123/3) )) / 4 }}} 
{{{ x = ( 9 +- sqrt( 707.6667) )) / 4 }}} 
{{{ x = ( 9 + 26.602 )/4 }}}
{{{ x = 35.602/4 }}}
{{{ x = 8.9005 }}}
To nearest tenth, {{{ x = 8.9 }}}
check answer:
{{{ log(4,2x-7) + log(4,3x-3) = 4 }}}
{{{ log(4,2*8.9-7) + log(4,3*8.9-3) = 4 }}}
{{{ log(4,17.8-7) + log(4,26.7-3) = 4 }}}
{{{ log(4,10.8) + log(4,23.7) = 4 }}}
{{{ log(4, 10.8*23.7) = log(4,256) }}}
{{{ log(4, 255.96) = log(4,256) }}}
Looks close enough
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Note that {{{x}}} had to be positive because a log
with a positive base (4), can't result in a negative number