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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.
So why are logarithms useful? Sometimes you might want to compare items that are so di erent from each other, that it becomes di cult. For example, let us say that we wanted to compare the sizes of the major bodies of the solar system. We want to communicate clearly, so we decide to make a graph of the volumes in cubic megameters (Mm). (A ...
Logarithms are very useful mathematical entities that have an enormous amount of application to real-world situations. Combined with their inverse relationship to the exponential functions, logarithms allow for the simplification of complex problem situations to basic arithmetic operations.
We use can logarithms to solve exponential equations: = b is x = log a bFor example, the solution of ex. 2 is x = log e 2. To find the value of this logarithm, we need to use a calculator. log e 2 = 0.6931.Note Logarithms were invented and used for solving exponential equations by the Scottish baron John Napi.
We now know that a logarithm is perhaps best understood as being closely related to an exponential equation. In fact, whenever we get stuck in the problems that follow we will return to this one simple insight. We might even state a simple rule.
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.
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).
