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•solve simple equations requiring the use of logarithms. Contents 1. Introduction 2 2. Why do we study logarithms ? 2 3. What is a logarithm ? if x = an then log a x = n 3 4. Exercises 4 5. The first law of logarithms log a xy = log a x+log a y 4 6. The second law of logarithms log a xm = mlog a x 5 7. The third law of logarithms log a x y ...
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.
We have the following de nition of logarithms: 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. 6).
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.
While we have introduced logarithms with a changeable base, there are two main bases that are found on most scienti c calculators, and are used more than others. Firstly, the common logarithm, most commonly written as just log(x).
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.
