Question

Simplify the expression below

Answer 1

\[\log_ \frac{ (x+3)^2 }{ (x-2)(x^2+5)^4}\]

Answer 2

That came out really small but I am new to using open study so

Answer 3

So far I have 2log(x+3) - log(x-2) + 4log(x^2+5)
Did I do it right?

Answer 4

First of all, we must determine what base the logarithm is. Would I be correct in assuming it is 10?

Answer 5

yes i think so

Answer 6

So, you are on the right track here (if division you subtract the log, if multiplication you add it), however notice that the two values in the denominator are together. So, they will need to be grouped and subtracted together.

Answer 7

Imagine, 2log(x+3) - (log(x-2) + 4log(x^2+5))

Answer 8

Yeah i just realized that i messed up with the bottom.
2log(x+3)-log(x-2)+4log(x^2+5)

Answer 9

@unknownunknown

Answer 10

So this is still the same answer as before. Remember to distribute the negative sign to the two remaining Log terms on the right.

Answer 11

confused

Answer 12

2log(x+3) - (log(x-2) + 4log(x^2+5)) = 2log(x+3) - log(x-2) + 4log(x^2+5)

Note the parentheses.

Answer 13

Correction: 2log(x+3) - (log(x-2) + 4log(x^2+5)) = 2log(x+3) - log(x-2) - 4log(x^2+5)

Answer 14

why is there a parenthesis??