Question

Solve for x
3^x = e^2

Answer 1

\[3^{x} = e ^{2}\]
Show work

Answer 2

i would get the square root of both sides first to make e alone...

\[\large \sqrt{3^x} = e\] do you understand that?

Answer 3

I don't have to use ln?

Answer 4

you will

Answer 5

i'll simplify this into \[\large 3^{x/2} = e\] you understand that algebra right?

Answer 6

first of all e=2.71828
so 2.71828^2=3^x
7.38905=3^x
x=1.82048

Answer 7

Where did you get the 7.389..?
When do I use ln?

Answer 8

\[\large 3^{x/2} = e\] \[\log_e 3 = \frac{x}{2}\] \[\ln 3 = \frac{x}{2}\] \[x = 2\ln 3\] \[x = \ln 3^2\] \[x = \ln 9\]

Answer 9

http://www.wolframalpha.com/input/?i=3^x+%3D+e^2

Answer 10

Its telling me the answer should be 2/ln 3= 1.820

Answer 11

take the natural log to start off with right away.

you'll get

ln3^x = 2

when you have a log raised to a power, you can bring the power down

x * ln3 = 2

get x by itself

x = 2/ln3

ta - daaaaaaaaaaa

Answer 12

:D lol thanks!