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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
•explain what is meant by a logarithm •state and use the laws of logarithms •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 ...
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 ( ) = , where 0 < -b is called the base and x is called the exponent. < 1, or > 1.
When asked to solve a logarithmic equation such as or the first thing we need to decide is how to solve the problem. Some logarithmic problems are solved by simply dropping the logarithms while others are solved by rewriting the logarithmic problem in exponential form.
Understanding Logarithms Intuitively. Adam A. Smith. Logarithms make a lot of people anxious. A lot of this has to do with the way they're often taught in high school and secondary school: by memorizing all the proper steps, without imparting much deeper meaning. For example, maybe you were once taught to solve problems like this: log7 49 = ?
We then use the rules of logarithms to simplify the expression. First use log(ab) = log a + log b We can now use log a k = k log a to get rid of the powers. Expand the brackets and collect the terms containing x on one side. Use the rules of logarithms to write the solution in the correct form: logl og log logl og log ab l b ab l a b b = b ...
Having previously defined what a logarithm is (see the notes on Functions and Graphs) we now look in more detail at the properties of these functions. The relationship between logarithms and exponentials is expressed as:
