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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 ...
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 = ?
to logarithms. In the lessons to follow we will learn some important properties of logarithms. One of these properties will give us a very important tool which we need to solve exponential equations. Until then let’s practice with the basic themes of this lesson.
To find the value of a logarithm we need to solve an exponential equation. Example (a) The solution of 2x = 8 is x = 3. We can write this in logarithm notation as log 2 8 = 3 ‘log of 8 to base 2 is 3’ (b) x = 5 is the solution of 2x = 32. We can write this using logarithms as log 2 32 = 5 ‘log of 32 to base 2 is 5’ (c) 102 = 100.
Learning Goal: We are learning that a logarithm is the inverse of the exponential function. In grade 11 Functions, you spent a bunch of time considering Exponential Functions, and it seems like a good idea to spend a little time reviewing that type of function. There are two methods.
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).
Essential Question. What are some of the characteristics of the graph of a logarithmic function? Every exponential function of the form f (x) bx, where b is a positive real number. = other than 1, has an inverse function that you can denote by g(x) = logb x. This inverse function is called a logarithmic function with base b.