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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.
The laws of logarithms. The three main laws are stated here: . First Law. log A + log B = log AB. . This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm of the product of A and B, that is log AB. For example, we can write. log10 5 + log10 4 = log10(5 × 4) = log10 20.
The laws of logarithms. The three main laws are stated here: . First Law. log A + log B = log AB. . This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm of the product of A and B, that is log AB. For example, we can write. log10 6 + log10 2 = log10(6 × 2) = log10 12.
a > 0, a 6= 1 and b > 0 we have: loga b = c , ac = b. 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.
Use of the Rules of Logarithms. In this section we look at some applications of the rules of logarithms. Examples 5 (a) log. 41 = 0: (b) log. 1010 = 1: (c) log. 10125 + log. 108 = log. 10. (125 8) = log.
Logarithms. If a > 1 or 0 < a < 1, then the exponential function f : R ! (0, defined 1) as f (x) = ax is one-to-one and onto. That means it has an inverse function. If either a > 1 or 0 < a < 1, then the inverse of the function ax is. loga : (0, 1) ! and it’s called a logarithm of base a. That ax and loga(x) are inverse functions means that ...
Taking logarithms is the reverse of taking exponents, so you must have a good grasp on exponents before you can hope to understand logarithms properly. We begin the study of logarithms with a look at logarithms to base 10.
