SOLUTION: I want to know how to simplify this...ln(e^(5AB)) thank you!!

Question 487084: I want to know how to simplify this...ln(e^(5AB))
thank you!!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
ln(e^(5AB) is equal to:
5AB * ln(e)
ln(e) is equal to 1
therefore your expressions simplifies to:
5AB.

if we let A = 2 and B = 3, then 5AB = 5*2*3 = 30
your equation is then:
ln(e^(30))
you can solve it directly using your calculator or you can solve it by simplifying it as we did before.
use your calculator to find ln(e^30))
it should be the same answer as 30*ln(e) which is equal to 30.
i did on mine and the answer i got was 30.

they're the same, as they should be.

i don't believe you can simplify it any further than that.
your answer is:
ln(e^(5AB)) = 5AB * ln(e) = 5AB

you are using one of the basic laws of logarithms that states:

log(a^x) = x*log(a)

RELATED QUESTIONS
Hey I want to know how to evaluate these expressions. A)e^ln 23 B) e^9 ln pie sign (answered by ikleyn)

I need the derivative of : y = e^x - e^-x The answer is supposed to be y' = e^x +... (answered by Alan3354)

Can Ya'll please help? I know how to simplify this but not to solve this. e^x=2 is... (answered by Alan3354)

Use logarithmic differentiation to solve: f(x) =(x^(3/2)*e^(-(x^2)))/(1-e^(x)) Don't (answered by jim_thompson5910)

Please help me solve this logarithm equation.. & can you do it step by step?? I want to... (answered by Fombitz)

i need help to simplify fully this logarithm expression, please...... (answered by Theo)

I need the derivative of : y = 1 / log x The answer is supposed to be y' = -ln 10 /... (answered by Edwin McCravy)

I am particular to doing the e^ln to each side of a number. And this problem is... (answered by fractalier,MathTherapy)

Hi Tutor, I am stuck on this problem. ln(x+2)-ln(4)=-ln x Do I take the ln of 2 and... (answered by nerdybill)