# logarithms

• March 24th 2010, 03:57 AM
tim_mannire
logarithms
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)

• March 24th 2010, 04:26 AM
masters
Quote:

Originally Posted by tim_mannire
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?

Hi tim_mannire,

Just take the natural log of both sides.

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

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

$3x-4=1-2x$

Quote:

Originally Posted by tim_mannire
ln(x) = 2ln(2)+ln(15)-ln(10) (for x>0)

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

Quote:

Originally Posted by tim_mannire
ln(3x-2) = 3 (x>2/3)

$e^3=3x-2$