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Logarithms are the mathematical function that is used to represent the number (y) to which a base integer (a) is raised in order to get the number x: x = ay; where y = loga(x). Most of you are familiar with the standard base-10 logarithm: y = log10(x); where x = 10y.
Most simply, logarithms are mathematical functions that extract the exponent from the exponential representation of a number. Antilogarithms (exponential functions) are literally functions that “undo” the taking of a logarithm.
explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms. Contents. Introduction. Why do we study logarithms ? What is a logarithm ? if x = an then loga x = n. 4. Exercises. 5. The first law of logarithms. loga xy = loga x + loga y. 6. The second law of logarithms.
à Definition of logarithm. To begin, recall that the logarithm base 10 of x is the power to which 10 is raised to equal x, x = 10log10HxL. In the natural logarithm has the base following, logH...L means logarithm base 10. We also will use the natural logarithm.
Chapter 1: Logarithms Used to Calculate Products ..... 1 Chapter 2: The Inverse Log Rules ..... 9 Chapter 3: Logarithms Used to Calculate Quotients ..... 20
A logarithm is just an index. We use log as an abbreviation for the word logarithm. 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.
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