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There are three laws of logarithms which you must know. log a x + log a y = log a ( xy ) where a , x , y > 0 . If two logarithmic terms with the same base number (a above) are being added together, then the terms can be combined by multiplying the arguments (x and y above). log 5 4 ) 2 × 4 = log 5 8. where a , x , y > 0 .
Example 1: Use Logarithm Rules Expand using logarithm rules until no more can be applied. We see that the argument is first and foremost a product. Therefore, we will use the Product Rule first. There are also some exponents. Please observe that can be written as . Therefore, we can write the following:
1 EXPONENTS AND LOGARITHMS WHAT YOU NEED TO KNOW • The rules of exponents: • ma m× an = a +n • a a a m n = mn • (am)n mn= a • aa m n n m • a a n n − = 1 • an × nb = (ab)n • a b a b n n n = ⎛ ⎝⎜ ⎛ ⎝ ⎞ ⎠⎟ ⎞ ⎠ • The relationship between exponents and logarithms: • ab=⇔b xb g a where a is called the ...
Sometimes we call it an exponent. Sometimes we call it an index. In the expression 24, the number 2 is called the base. Example We know that 64 = 82. In this example 2 is the power, or exponent, or index. The number 8 is the base. 2. Why do we study logarithms ? In order to motivate our study of logarithms, consider the following: we know that ...
This topic introduces logarithms and exponential equations. Logarithms are used to solve exponential equations, and so are used along with exponential functions when modelling
In this booklet we will demonstrate how logarithmic functions can be used to linearise certain functions, discuss the calculus of the exponential and logarithmic functions and give some useful applications of them.
The rules for the behaviour of exponents follow naturally from this definition. First, let’s try multiplying two numbers in exponential form. For example 23 ×24 =(2×2×2)×(2×2×2×2) =2×2×2×2×2×2×2 7 factors =27 =23+4. Examples like this suggest the following general rule. Rule 1: bn ×bm = bn+m.
