Properties of Logarithms

This material should be review, but is provided here for your reference.

Our relationship is

T = 2 \pi \left( \frac{L}{g} \right)^p

We want to use logarithms to convert this to a line (because we know how to fit a line!). First, it may be helpful to review some properties of logarithms.

Logarithm Properties

The three major logarithm properties we use are the following product, quotient, and power rules. For a more in depth review, visit this chapter of OpenStax College Algebra on Logarithmic Properties.

 

THE PRODUCT RULE FOR LOGARITHMS

The product rule for logarithms can be used to simplify a logarithm of a product by rewriting it as a sum of individual logarithms:

logb(MN)=logb(M)+logb(N) for b>0

 

THE QUOTIENT RULE FOR LOGARITHMS

The quotient rule for logarithms can be used to simplify a logarithm or a quotient by rewriting it as the difference of individual logarithms:

logb(M/N)=logb(M)−logb(N)

 

THE POWER RULE FOR LOGARITHMS

The power rule for logarithms can be used to simplify the logarithm of a power by rewriting it as the product of the exponent times the logarithm of the base:

logb(Mn)=nlogb(M)

 

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Physics 132 Lab Manual by Brokk Toggerson and Aidan Philbin is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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