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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. 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.
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 and Logarithmic 6.3 Functions. Essential Question. What are some of the characteristics of the graph of a logarithmic function? Every exponential function of the form f (x) bx, where b is a positive real number. = other than 1, has an inverse function that you can denote by g(x) = logb x.
De nition. a > 0, a 6= 1 and b > 0 we have: loga b = c , ac = b. Secondly loga b = c means a raised to the power of c is equal to b. So if we want to calculate loga b, we need to nd a number to which we need to raise a to to get b. We will practice the above de nition in this presentation. Calculate log1 81. 3.
Log table (logarithm table) is used in performing bigger calculations (of multiplication, division, squares, and roots) without using a calculator. The logarithm of a number to a given base is the exponent by which that base should be raised to give the original number.
single logarithm. log 2 7 + log 2 2. log 2 20 − log 2 4. 3log 5 2 + log 5 8. 2log 6 8 − 5log 6 2. log 10 8 + log 10 5 − log 10 0.5. log 2 14 , log 2 5 , log 5 64 , log 6 2 , log 10 80. single logarithm. log 3 5 + log 3 2.
Chapter 1: Logarithms Used to Calculate Products ..... 1 Chapter 2: The Inverse Log Rules ..... 9 Chapter 3: Logarithms Used to Calculate Quotients ..... 20
