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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 ...
logs.” “The log of a quotient is the difference of the logs.” The students see the rules with little development of ideas behind them or history of how they were used in conjunction with log tables (or slide rules which are mechanized log tables) to do almost all of the world’s scientific and
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.
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. That ax and loga(x) are inverse functions means that ...
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.
Exponentials and Logarithms. This chapter is devoted to exponentials like 2x and 10x and above all ex: The goal is to understand them, differentiate them, integrate them, solve equations with them, and invert them (to reach the logarithm). The overwhelming importance of ex makes this a crucial chapter in pure and applied mathematics.
Here are corresponding formulas for logarithms: (1) log b(xy) = log b x+ log b y for x;y > 0; (2) log b x y = log b x log b y for x;y > 0; (3) log b(x y) = ylog b x for x > 0: To derive each of the formulas in (1){(3) we rely on the characteristic property of a logarithm value: log b x is the only number y satisfying the equation by = x. Proof ...
