## anonymous one year ago Write the following expression as a single logarithm: 2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)

1. Nnesha

quotient rule$\large\rm log_b x - \log_b y = \log_b \frac{ x }{ y}$ to condense you can change subtraction to division product rule $\large\rm log_b x + \log_b y = \log_b( x \times y )$ addition ----> multiplication power rule $\large\rm log_b x^y = y \log_b x$

2. anonymous

i get the first half of it but not the second where it begins +5log

3. Nnesha

there is a negative sign so apply quotient rule after power rule

4. anonymous

top half if log(x+3)^2(x-7)^3 right?

5. anonymous

+5log(x-2)-log(x^2) i need help with this part

6. Nnesha

$\large \rm 2log(x+3)\color{red}{-}3log(x-7)\color{red}{+}5log{x}-2)\color{red}{-}log(x^2)$ first of all power rule $\large\rm log(x+3)^2\color{ReD}{ -}log(x-7)^3\color{reD}{+} log(x-2)^5\color{ReD}{-}log(x^2)$ now apply quotient rule for negative one and product rule for log(x-2)^2

7. Nnesha

sorry my internet got disconnected

8. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @nsquared22 top half if log(x+3)^2(x-7)^3 right? $$\color{blue}{\text{End of Quote}}$$ (x-7)^3 should be at the bottom bec it's log (x+3)^2 MINUS log(x-7)^3

9. Nnesha

$\log \frac{ (x+3)^2 }{ (x-7)^3 } + \log (x-3)^5 -\log (x^2)$ change addition sign to multiplication and subtraction with division

10. Nnesha

let me know if you need more help :)