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Chapter 5Logarithm, Exponential, and Trigonometric Functions

The logarithm, exponential, and trigonometric functions play a fundamental role in all fields of science and are particularly useful in Islamic finance. The logarithm and exponential functions are related; one implies the other. The trigonometric functions play an important role in measuring slopes, direction, and rates of change of a function and have wide applications in statistics such as in time series analysis.

Logarithm Functions

Consider the quantity . Obviously, we have three numbers involved: the multiplicand 2, the exponent 4, and the product 16. From this operation we may make the following statement: the exponent 4 is the logarithm of 16 with base 2. Likewise, we may consider the following quantity: . We can make the statement that the exponent 5 is the logarithm of 100,000 with base 10. More generally, if

(5.1) then is the logarithm of with base , and is written

(5.2)

Accordingly, we write

and

The logarithm ...

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