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This topic introduces logarithms and exponential equations. Logarithms are used to solve exponential equations, and so are used along with exponential functions when modelling
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.
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 a Logarithm. In the last chapter we solved and graphed “exponential equations.” The strategy we used to solve those was to make the bases the same, set the exponents equal, and solve the resulting equation. You might wonder what would happen if you could not set the bases equal?
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. We have the following de nition of logarithms: De nition. a > 0, a 6= 1 and b > 0 we have:
Introduction to Logarithms used whole number bases for the logarithms, including base 10, which is called the common logarithm. Another logarithm, the natural logarithm, uses the number e as the base. The number e is a constant, and, like another famous constant π, e is an irrational number.
The logarithm gives us the exponent necessary to produce a desired result. Logarithms answer the question: “What power of the base is required to produce a given value?” In our example, the logarithm of one million base ten is six, and the notation looks like this: log101,000,000 = 6.
