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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.
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?
Chapter 1: Logarithms Used to Calculate Products ..... 1 Chapter 2: The Inverse Log Rules ..... 9 Chapter 3: Logarithms Used to Calculate Quotients ..... 20
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).
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.
A Logarithm is the inverse function for an Exponent -We remember that inverse functions do the exact opposite of one another. -An example can be seen in the table above; the exponential function sends −2 to 1
