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Express the given quantity as a single logarithm.

$\frac{1}{3} \ln (x+2)^{3}+\frac{1}{2}\left[\ln x-\ln \left(x^{2}+3 x+2\right)^{2}\right]$

$\ln \left(\frac{\sqrt{x}}{x+1}\right)$

Calculus 1 / AB

Chapter 1

Functions and Sequences

Section 5

Logarithms; Semilog and Log-Log Plots

Functions

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University of Michigan - Ann Arbor

University of Nottingham

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Okay, so we're well said by multiplying out at 1/2 here. Okay, I know it's noticed that we have constants in front of our natural are log so we can bring that into our power. Okay, so that gives me Ellen of X Plus two, three times 1/3 is one. And then we have a line of extra pair of 1/2 and then minus Ellen of X squared plus three x Plus two. And now we see that we have some here. So it's combined that into a product that's Owen of exports to times extra pair of 1/2 minus Ellen of X squared. Plus three experts still, and that's contracted out into exports to in an X Plus one. So we have a difference between these two. So it's rewrite this as a quotient. Okay, so we feel that are exposed once, cancel and we're left with the natural log of extra crab, 1/2 over X plus one

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