Thread: Natural Logs/ Logarithms?

Hi!
I am taking AP Calc AB and my new teacher sent us a math assignment to do over the summer.

There is this question that stumped me.

Evaluate or simplify

a. ln Ce^-at

I have never seen something like this in my life! I tried googling it but no answer. Obviously it has something to do with logarithms and natural logs because of the "ln". How would I simplify/evaluate?

Just to check my work for letter b the problem is:

log4 (1/8)

that would be 4^x= 1/8 right?

Thanks!

a. ln Ce^-at


ln a^b=b ln a

ln Ce^-at = -at ln Ce

ln(a * b) =ln a + ln b


ln Ce^-at = -at ln Ce = -at(lnC + ln e)

ln e=1

ln Ce^-at = -at ln Ce = -at(lnC + ln e)=-at(lnC+1)

Are C and e different symbols? Could you please clarify with parentheses?