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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 (𝑥)=𝑏𝑥, where 0<𝑏<1, or 𝑏>1. -b is called the base and x is called the exponent.
This topic introduces logarithms and exponential equations. Logarithms are used to solve exponential equations, and so are used along with exponential functions when modelling growth and decay. The logarithmic function is an important mathematical function and you will meet it again if you study calculus.
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.
We have the following de nition of logarithms: De nition For a > 0, a 6= 1 and b > 0 we have: log a b = c ,ac = b 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 ...
The most important thing to know about logarithms is this: 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.
1.1 Introduction Whenever we use expressions like 73 or 25 we are using exponents. The symbol 25 means 2×2×2×2×2 5 factors. This symbol is spoken as ‘two raised to the power five’, ‘two to the power five’ or simply ‘two to the five’. The expression 25 is just a shorthand way of writing ‘multiply 2 by itself 5 times’.
2D Introduction to logarithms. In this section we shall look at an operation which reverses the ef ect of exponentiating (raising to a power) and allows us to fi nd an unknown power. If you are asked to solve. x2 3 f x ≥ 0.
