Αποτελέσματα Αναζήτησης
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.
Precalculus Tutorials. Introduction to Logarithms. -A logarithm is the inverse function for an exponent; therefore, we will review exponential functions first. Review of Exponential Functions. -An exponential function has the general form ( ) = , where 0 < -b is called the base and x is called the exponent. < 1, or > 1.
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. So the expressions like log1 3, log 2 5 numbers (similarly to expressions like. p or log4( 6).
The change of base rule: log a. c. = log. c b. There are two common abbreviations for logarithms to particular bases: log. 10 x is often written as log x. loge x is often written as ln x. The graphs of exponential and logarithmic functions:
x. = a ⇔ x ga b It is worth noting that the two most common bases have abbreviations for their logarithms. Since we use a decimal system of counting, 10 is the default base for a logarithm, so log x is usually written simply as log x and is called the. 10. ‘common logarithm’.
Logarithms. Study the statement. 100 = 102. In this statement we say that 10 is the base and 2 is the power or index. Logarithms provide an alternative way of writing a statement such as this. We rewrite it as. log10 100 = 2. This is read as ‘log to the base 10 of 100 is 2’. These alternative forms are shown in Figure 1.
LESSON 10 LOGARITHMIC FUNCTIONS. Definition The logarithmic function with base b is the function defined by. f ( x ) log x , where b 0 and b 1. b . Recall that y log y. b x if and only if b x. Recall the following information about logarithmic functions: 1. The domain of f ( x ) log.
