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After reading this text and / or viewing the video tutorial on this topic you should be able to: explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms.
abbreviations for their logarithms. Since we use a decimal system of counting, 10 is the default base for a logarithm, so log 10 x is usually written simply as log x and is called the ‘common logarithm’. Also, the number e that we met in section 2C is considered the ‘natural’ base, so the base-e logarithm is
What does it mean? First of all the assumptions (restrictions) are important. The number a, called the base of the logarithm, has to be greater than 0 and cannot be equal to 1. The number b (which we take the logarithm of) has to be greater than 0. So the expressions like log1 3, log 2 5 numbers (similarly to expressions like. p or log4( 6).
Precalculus Tutorials. Introduction to Logarithms. -A logarithm is the inverse function for an exponent; therefore, we will review exponential functions first. Review of Exponential Functions. -An exponential function has the general form ( ) = , where 0 < -b is called the base and x is called the exponent. < 1, or > 1.
Definition of the Logarithmic Function. log x y ay x where “a” is a positive number and a 1. a. In words, log. a. x is the exponent to which the base “a” must be raised to give “x”.
A logarithm represents the scale of a number. Think of all the one-digit numbers, 1 through 9. (For now we're skipping over 0.) Of course these numbers are all di erent, but they're close enough to each other to be easily comparable. However the two-digit numbers, 10 through 99, are on a totally di erent scale. They're easily comparable to each.
This topic introduces logarithms and exponential equations. Logarithms are used to solve exponential equations, and so are used along with exponential functions when modelling
