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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.
traditional study of logarithms, we have deprived our students of the evolution of ideas and concepts that leads to deeper understanding of many concepts associated with logarithms. As a result, teachers now could hear “(5.2)y = 30.47, y = 6.32 because the calculator says so,” (52 = 25 for goodness sakes!!)
We want to have logarithms involving just one base so that we can apply the rules of logarithms. Here we use the change of base rule to turn logs with base x into logs with base 4. (Alternatively, we could have turned them all into base x instead.) Multiply through by log 4 x to get the log terms together. Take the square root of both sides ...
These scales of size 10 are the base-10 logarithms, which are represented by \log10" in equations. Base-10 logarithms are sometimes called common logarithms. That small \10" is the base, and it can be any positive number except 1 (though we'll soon see that only a few bases are commonly used).
Introduction to Logarithms. In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number? Example: How many 2 s multiply together to make 8? Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2 s to get 8. So the logarithm is 3. How to Write it. We write it like this: log2(8) = 3.
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.
Suppose we begin with a number and we wish to find the power to which 10 must be raised to obtain that number. For example, suppose we begin with the number 7 and we wish to find the power to which. 10 must be raised to obtain 7. This number is called the logarithm to the base 10 of 7 and is written log. 10 7.
