Question 29425
ln(x+2)=ln(2x-1)+3
ln(x+2) - ln(2x-1) = 3
{{{ ln((x+2)/(2x-1)) = 3 }}}
{{{ (x+2)/(2x-1) = e^3 }}}


Now, {{{e^3}}} is just a number...JUST a number!


So,
{{{ (x+2) = e^3(2x-1) }}}
{{{ x+2 = 2e^3x-e^3 }}}
{{{ x+2-2e^3x = -e^3 }}}
{{{ x-2e^3x = -2-e^3 }}}
{{{ x(1-2e^3) = -2-e^3 }}}
{{{ x = (-2-e^3)/(1-2e^3) }}}
{{{ x = (-(2+e^3))/(-(2e^3-1)) }}}
{{{ x = (2+e^3)/(2e^3-1) }}}


so either leave this as it is...it is the PRECISE answer. If you use a calulator, you will have to round up the answer, since it is a never-ending number... x = 0.563822605 to 9dp.


PS the other solution by sdmmadam is wrong because on line 3 the "ln" becomes "log" which is wrong. The actual mechanics is correct though...just that the x value is wrong.


jon.