Question

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

Answer 1

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 \[\large\rm log_b x^y = y \log_b x\]

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

\[\large \rm 2log(x+3)\color{red}{-}3log(x-7)\color{red}{+}5log{x}-2)\color{red}{-}log(x^2)\] 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

Answer 7

sorry my internet got disconnected

Answer 8

\(\color{blue}{\text{Originally Posted by}}\) @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

Answer 9

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

Answer 10

let me know if you need more help :)