Question

Solve 3^(4x-7)=4^(2x+3)

Answer 1

(4x-7)*ln(3) = (2x+3)*ln(4)

Answer 2

4x*ln(3)-2x*ln(4) = 3*ln(4)+7*ln(3)

Answer 3

\[3^{4x-7}=4^{2x+3}\]\[\ln(3^{4x-7})=\ln(4^{2x+3})\]\[(4x-7)(\ln3) = (2x+3)(\ln4)\]\[4xln3-7\ln3 = 2xln4 +3\ln4\]\[4xln3-2xln4 = 3\ln4+7\ln3\]\[x(4\ln3-2\ln4) = 3\ln4+7\ln3\]\[x = \frac{3\ln4 +7\ln3}{4\ln3-2\ln4} \approx 7.305\]

Answer 4

I love logarithms!

Answer 5

Hey alexray19, why did you go from
\[4xln3−7\ln3=2xln4+3\ln4\]
to
\[4xln3−2xln4=3\ln4+7\ln3\] I'm a bit confused.

Answer 6

It's algebra

Answer 7

It's just algebra; I rearranged the equation by subracting 2xln4 from both sides and adding 7ln3 to both sides.

Answer 8

That way I had all of the terms with x in them on one side and all of the terms without x on the other side.

Answer 9

OH! I see now! Thank you!

Answer 10

jbeloy17, get a piece of scrap paper and bring all the like terms on one side and the other like terms on the other side. It'll be good practice for preparing for your pre-calc exam

Answer 11

Thanks kumar2006!