anonymous
  • anonymous
Write the following expression as a single logarithm: 2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)
Mathematics
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anonymous
  • anonymous
Write the following expression as a single logarithm: 2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)
Mathematics
chestercat
  • chestercat
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Nnesha
  • 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 \[\large\rm log_b x^y = y \log_b x\]
anonymous
  • anonymous
i get the first half of it but not the second where it begins +5log
Nnesha
  • Nnesha
there is a negative sign so apply quotient rule after power rule

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anonymous
  • anonymous
top half if log(x+3)^2(x-7)^3 right?
anonymous
  • anonymous
+5log(x-2)-log(x^2) i need help with this part
Nnesha
  • 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
Nnesha
  • Nnesha
sorry my internet got disconnected
Nnesha
  • 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
Nnesha
  • 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
Nnesha
  • Nnesha
let me know if you need more help :)

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