Question

Simplify the expression below and write it as a single logarithm:

Attached.

Answer 1

when logs have the same base (as all the logs in your equation do) you can combine them like you would combine like terms EXCEPT, addition is the same as multiplying, and subtraction is the same as division

so, if you had log2+log3 you could write that as log(2*3) or log 6

and if you had log2-log3 you could write that as log (2/3)

this holds when you are working with variables as well

logx+logy=log(xy) and logx-logy=log(x/y)

Answer 2

I get what you are saying but i dont know how to start this problem. 3log(x+4). what do i do with x+4? just separate it?

Answer 3

no, you're going to take it and multiply it with another term, so if you have x+4 you might multiply it with x+2 (I'm not looking at the problem right now, that's just an example) to get x^2 + 6x + 8 and then you would have log(x^2 + 6x + 8)

then just add up the coefficients

Answer 4

but what if there are logs in front of every group of parenthesis? there isnt just one. i cant do that

Answer 5

I guess I'm not explaining it very well, so I"m just gonna show you the work

Answer 6

3log(x+4) - 2log(x-7) + 5log(x-2) - log(x^2)

**I made a mistake above, the coefficients of logs are basically like exponents, so 3log(x+4)=log(x+4)^3


the positive logs are the ones you are going to multiply so multiply the parts in parentheses, the options don't have them multiplied out, so I'm just going to write it how it is going to be shown in the multiple choice

(x+4)^3 * (x-2)^5

the negative logs are the ones you are going to divide the equation by, so basically you are going to write your answer as a fraction, with the product of the positives as the numerator, and the product of the negatives as the denominator

your denominator is going to be:

(x-7)^2 * (x)^2

the final equation is going to look like this:

log(((x+4)^3 * (x-2)^5)/((x-7)^2 * (x)^2)) which goes with the first choice

Answer 7

thanks