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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.
Logarithms. Study the statement. 100 = 102. In this statement we say that 10 is the base and 2 is the power or index. Logarithms provide an alternative way of writing a statement such as this. We rewrite it as. log10 100 = 2. This is read as ‘log to the base 10 of 100 is 2’. These alternative forms are shown in Figure 1.
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.
2D Introduction to logarithms. In this section we shall look at an operation which reverses the ef ect of exponentiating (raising to a power) and allows us to fi nd an unknown power. If you are asked to solve. x2 3 f x ≥ 0.
Logarithms were originally developed to simplify complex arithmetic calculations. They were designed to transform multiplicative processes into additive ones.
A logarithm represents the scale of a number. Think of all the one-digit numbers, 1 through 9. (For now we're skipping over 0.) Of course these numbers are all di erent, but they're close enough to each other to be easily comparable. However the two-digit numbers, 10 through 99, are on a totally di erent scale. They're easily comparable to each.
Introduction to Logarithms used whole number bases for the logarithms, including base 10, which is called the common logarithm. Another logarithm, the natural logarithm, uses the number e as the base. The number e is a constant, and, like another famous constant π, e is an irrational number.
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