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•explain what is meant by a logarithm •state and use the laws of logarithms •solve simple equations requiring the use of logarithms. Contents 1. Introduction 2 2. Why do we study logarithms ? 2 3. What is a logarithm ? if x = an then log a x = n 3 4. Exercises 4 5. The first law of logarithms log a xy = log a x+log a y 4 6. The second ...
Chapter 1: Logarithms Used to Calculate Products ..... 1 Chapter 2: The Inverse Log Rules ..... 9 Chapter 3: Logarithms Used to Calculate Quotients ..... 20
We have the following de nition of logarithms: De nition For a > 0, a 6= 1 and b > 0 we have: log a 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 ...
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.
This topic introduces logarithms and exponential equations. Logarithms are used to solve exponential equations, and so are used along with exponential functions when modelling
Logarithm formulas. = loga x () ay = x (a; x > 0; a 6= 1) loga 1 = 0. loga a = 1. loga(mn) = loga m + loga n. m. loga = loga m. n.
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.
