Αποτελέσματα Αναζήτησης
Logarithms Definition of the Logarithmic Function x y a y x log a where “a” is a positive number and az1 In words, log a x is the exponent to which the base “a” must be raised to give “x”. Example: log 8 3 23 8 2 Logarithmic form Exponential form The word “log” asks: What power do I put on 2 to get 8? Answer: 3
This topic introduces logarithms and exponential equations. Logarithms are used to solve exponential equations, and so are used along with exponential functions when modelling
solve simple equations requiring the use of logarithms. Why do we study logarithms ? What is a logarithm ? 4. Exercises. 5. The first law of logarithms. 6. The second law of logarithms. 7. The third law of logarithms. 8. 9. 10. 11. 12. 13. 14. 1. Introduction. In this unit we are going to be looking at logarithms.
number not involving a logarithm. a) log 24 log 32 2− b) log 96 3log 2 log 43 3 3− − c) 5 5 5 1 2 log 500 log log 10 5 + − d) 2log 54 log 0.25 4log 23 3 3− − e) 8log 2 log 4 3log 96 6 6− −( ) 3 , 1 , 3 , 6 , 6
Taking logarithms is the reverse of taking exponents, so you must have a good grasp on exponents before you can hope to understand logarithms properly. We begin the study of logarithms with a look at logarithms to base 10.
We have the following de nition of logarithms: 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. 6).
A Logarithm is the inverse function for an Exponent -We remember that inverse functions do the exact opposite of one another. -An example can be seen in the table above; the exponential function sends −2 to 1 4. The logarithm would send 1 4 back to −2. -Inverse functions undo one another and this concept is going to be crucial to calculating
