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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
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.
This topic introduces logarithms and exponential equations. Logarithms are used to solve exponential equations, and so are used along with exponential functions when modelling
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.
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.
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.
