e^(3x) = 5
2007-08-20 11:53:05 · 5 answers · asked by lucy_loo_boo 1 in Science & Mathematics ➔ Mathematics
3x = ln 5, so that
x = (ln 5) / 3 = 0.536479... .
Live long and prosper.
2007-08-20 11:56:50 · answer #1 · answered by Dr Spock 6 · 0⤊ 0⤋
You know that log in base e is noted by ln.
So let's try to find the logarithm of both sides
We have e^(3x) = 5. Thus ln [e^(3x)] = ln (5)
Since ln a^n = n ln (a) . Hence, 3x ln(e) = ln(5)
ln e = 1 . Therefore, 3x (1) = ln 5 => 3x = ln 5
Divide both sides by 3 , we have 3x = ln 5 => x = ln(5)/ 3
You can leave the answer as it is. There are other ways also to get the answer depend of your knowledge in logarithms :)
2007-08-20 19:01:47 · answer #2 · answered by cool_black_stallion75 2 · 0⤊ 0⤋
The answer is 3x = ln(5) x = ln(5)/3
oh wow, how hilarious because I had the same exact problem for homework last night!!! lol =)
2007-08-20 19:11:22 · answer #3 · answered by Julia♥ 4 · 0⤊ 0⤋
3x = ln(5)
x = ln(5)/3
2007-08-20 18:57:20 · answer #4 · answered by gebobs 6 · 0⤊ 0⤋
e^x = y ===> x = ln(y)
so take ln for both sides
ln e^(3x) = ln(5)
3x = ln(5)
x = ln(5)/3
2007-08-20 18:58:23 · answer #5 · answered by 7 · 0⤊ 0⤋