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# Express the given quantity as a single logarithm.$\ln b + 2 \ln c - 3 \ln d$

## $\ln \left(\frac{b c^{2}}{d^{3}}\right)$

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

Okay. In order to change this quantity to a single lager them, we need to use properties of logarithms, one of which is the power property, which allows us to take these numbers here in front and bring them up and make them powers inside the log rhythm. And so now from that, we have the natural log of B plus the natural log of C squared minus the natural log of D cubed. Now we can use the product property, which tells us that if we have a log plus a log, we can combine it into the log of the product. So we have the natural log of B times C squared. Now we can use the quotient property, which tells us that if we have a log minus a log, we can combine those into the log of the quotient. So now we have the natural log of B C squared over D cubed

Oregon State University
##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp