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Express the given quantity as a single logarithm.

$ \ln b + 2 \ln c - 3 \ln d $

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01:03

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Missouri State University

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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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

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