Need to solve the following for x

e^(3x-4) = e^(1-2x) Do i figure out the logs first or do i combine the x terms?

ln(x) = 2ln(2)+ln(15)-ln(10) (for x>0)

ln(3x-2) = 3 (x>2/3)

thanks for your help

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- Mar 24th 2010, 03:57 AMtim_mannirelogarithms
Need to solve the following for x

e^(3x-4) = e^(1-2x) Do i figure out the logs first or do i combine the x terms?

ln(x) = 2ln(2)+ln(15)-ln(10) (for x>0)

ln(3x-2) = 3 (x>2/3)

thanks for your help - Mar 24th 2010, 04:26 AMmasters
Hi tim_mannire,

Just take the natural log of both sides.

$\displaystyle e^{3x-4}=e^{1-2x}$

$\displaystyle \ln e^{3x-4}=\ln e^{1-2x}$

$\displaystyle 3x-4=1-2x$

$\displaystyle x=e^{2\ln2+\ln15-\ln10}$

$\displaystyle e^3=3x-2$