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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.
We use log as an abbreviation for the word logarithm. To find the value of a logarithm we need to solve an exponential equation. Example (a) The solution of 2x = 8 is x = 3. We can write this in logarithm notation as log 2 8 = 3 ‘log of 8 to base 2 is 3’ (b) x = 5 is the solution of 2x = 32. We can write this using logarithms as log 2
The natural logarithm is often written as ln which you may have noticed on your calculator. lnx = loge x The symbol e symbolizes a special mathematical constant. It has importance in growth and decay problems. The logarithmic properties listed above hold for all bases of logs. If you see logx written (with no base), the natural log is implied.
In mathematics, the logarithm table is used to find the value of the logarithmic function. The simplest way to find the value of the given logarithmic function is by using the log table. Here the definition of the logarithmic function and procedure to use the logarithm table is given in detail.
log a 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. So the expressions like log 1 3, log p2 5 or log 4( 1) are not de ned in real
1. y = log a x ()ay = x (a;x > 0;a 6= 1) 2. log a 1 = 0 3. log a a = 1 4. log a (mn) = log a m+log a n 5. log a m n = log a m log a n 6. log a m n = nlog a m 7. log a m = log b mlog a b 8. log a m = log b m log b a 9. log a b = a log b a 10. log a x = lna lnx 1. Title: Math formulas for logarithmic functions Author: Milos Petrovic ( www ...
Find the value of y. 2. Evaluate. 3. Write the following expressions in terms of logs of x, y and z. 4. Write the following equalities in exponential form. 5. Write the following equalities in logarithmic form. 6. True or False? 7. Solve the following logarithmic equations. 8. Prove the following statements. 9.
