Expert: Sherman D. - 7/15/2004

Question
Write as a single logarithm:
log 2+3log x-(1/2)log b.
My book gives the answer, log(2x^3/sqrt(b)).
I got, (log(2*x^3)/log sqrt(b)).
If both are the same answer, please explain why.(I would think (log/log)=1).If they're not, please explain how to get the correct answer. Thank you.

Answer
if by this you mean

log(2) + 3(log(x)) - (1/2)log(b)

becomes

log(2) + log(x^3) - log(b^(1/2))

then

log((2 * x^3)/(b^(1/2)))

or

log((2x^3)/(sqrt(b))

since they all of the same base, you can just put them together as one.

For more information, go to people.hofstra.edu/faculty/Stefan_Waner/RealWorld/calctopic1/logs.html

What you got is kinda correct, but you can just right it as log((2x^3)/(sqrt(b)))

correction on what i said. Since they have the same base, you can combined them into one, which is correct, but what i didn't tell you is this.

Your answer of (log(2x^3))/(log(sqrt(b))) would be considered log(base b)(2x^3)