Simplify: ln e^4?

Question

Simplify: ln e^4

Answer 1

That is a natural logarithm with the base of e and if you have a power for your logarithm, it will move to the back of the logarithm like this:

Log.b(a^x) = a*Log.b(a).

So now you have:

Log.e(e^4) which will be simplified as:

4*Log.e(e)

And as long as:

Log.a(a) is equal to 1, you have:

4*1 = 4 so the answer is 4.

Good luck.

Answer 2

ln (4x) + ln (x) = 9 ln (4x^2) = 9 (using ingredients that ln M + ln N = ln (MN) convert to exponential (or exponentiate the two sides to base e) e^9 = 4x^2 e^9 / 4 = x^2 sqrt(e^9 / 4) = x (you would be able to discard the unfavourable root as extraneous) and sqrt(e^9 / 4) = 40 5.0086 (an extremely solid sort of the time i could particularly see the respond as sqrt(e^9 / 4)) **** edit: calculus, you made a mistake... ln 4x^2 =/= 2 ln 4x if it have been in parenthese, then ln (4x)^2 = 2 ln 4x because it truly is written, ln 4x^2 = ln 4 + ln x^2 = ln 4 + 2 ln x

Answer 3

move the 4 to the front.
lne=1
answer is 4

Answer 4

Would you believe the answer is 4.
Any log(base) base^power yields just the power.

Answer 5

nifty aint it
i luv math