Question

use the laws of logarithms to combine the expression.

Answer 1

\[1/3\log_{10}(x+2)^{3}+1/2[logx ^{4}-\log(x ^{2}-x-6)] \]

Answer 2

the answer in the book says:\[\log_{10}(x ^{3}/x-3)\]

Answer 3

\[\frac{1}{3}\log(x+2)^3=\log((x+2)^3)^{\frac{1}{3}}=\log(x+2)\]

Answer 4

\[\frac{1}{2}\left(\log(x^4)-\log(x^2-x-6)\right)\]
\[\frac{1}{2}\left(\log(x^4)-\log(x-3)(x+2)\right)\]
\[\frac{1}{2}\log\left(\frac{x^4}{(x-3)(x+2)}\right)\]

Answer 5

That's what i got when I first did the problem. but you have to move the 1/2 as a sqrt right?

Answer 6

hmm i can make a square root, but i am not sure how you are going to end up with the books answer. let me think...

Answer 7

ok

Answer 8

\[\log\left(\frac{x^4}{(x-3)(x+2)}\right)^{\frac{1}{2}}\]

Answer 9

oh maybe you can just add the fractions

Answer 10

yes and the (x+2) will cancel with the other one

Answer 11

I see it now

Answer 12

thanks

Answer 13

whew
yw