Logarithm/Exponents math problems help!?

Question

I'm hung up on these... its for a math summer review packet and I can't figure it out.

the directions say: "Rewrite using properties of logs and exponents"

ln(4xsinx)


and the other:

e^(3+x) (the carrot (^) indicates an exponent)

If you can help w/ step by step at least to get me started... that would be great.

Thanks

Answer 1

Not sure exactly what they want you to rewrite...but here is one way to rewrite them.
ln(ab) = ln(a) + ln(b), so
ln(4xsinx) = ln(4) + ln(x) + ln(sinx)

and e^(a+b) = (e^a)(e^b), so
e^(3+x) = (e^3)(e^x)

Answer 2

1) =4xsinx


2) e^(3+x)= e^(3+x)=y
ln e^y=3+x (put ln on both sides, cancel ln e)
y=ln(3+x)

Answer 3

Just in the interests of accuracy, I'd have to weigh in favor of the first respondent.

Answer 4

ln ( 4x ) + ln ( s ) + ln ( x )

( e^3 ) + ( e^x )

Its easy Im almost sure you dont need an explanation