In this set of Math Tutorials we cover Logarithms in detail with clear guides, Logarithms formulas and working examples. Each tutorial includes example questions, a revision guide and supporting Logarithms calculators.
We also provide online Logarithms Calculators which allow you to calculate specific Logarithms formula in support of the tutorials or to check and verify your own calculations in support of your Logarithms homework, math coursework or to help you improve your own understanding so it is easier to teach your children Logarithms.
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This chapter deals with logarithms - the inverse of exponents.
The first tutorial is an introduction to logarithms, where the most basic features of logarithms such as definition and components, how logarithms were invented, etc., are explained. The relationship between logarithms and exponents is also highlighted in the first part of this tutorial. It concludes by explaining how the properties of logarithms are combined to calculate the value of logarithmic expressions.
The second tutorial of this chapter deals with exponential and logarithmic equations. They are more challenging than linear, quadratic or cubic equations, as the variable lies in the exponent or argument of the logarithm. Hence, they need particular attention and explanation. For this reason, this tutorial addresses questions like: How many types of logarithmic equations are there? How to solve standard logarithmic equations? How to solve more advanced logarithmic equations?... and so on. However, the most important question addressed in this tutorial is: How to solve exponential equations using logarithms and vice versa?
The third tutorial focuses on modelling curves by means of logarithms. It begins with an introduction to functions (which we explain more in detail in the 16th chapter of this math course); then it continues by addressing questions like how to recognize a function, what are independent and dependent variables, what is the graph of a function, etc. The focus then shifts towards exponential functions and their components, including the graph. The same thing occurs with logarithmic functions as well. Another question addressed in the third tutorial is: How to find the original function when its graph is given? Last, this tutorial deals with the most important question it is intended for: How to make curves modelling using logarithms? However, this question is addressed after explaining what modelling curves mean and why modelling a curve is useful when studying exponential functions.
The fourth and last tutorial of this chapter deals with the natural logarithm (ln) function and its graph. It begins with the concept of Euler's number, its history and the method used to find and write it. Then, the tutorial continues with the meaning of natural logarithms and the rules applied when dealing with natural logarithms. Another element this tutorial focuses on is solving equations including natural logarithms. Last, questions like how to deal with ln functions; how to plot ln function graphs and how to make curves modelling using ln functions are addressed.
The following Math Calculators are provided in support of the Logarithms tutorials.