1. Lesson 3

1.4. Explore 3

Mathematics 30-2 Module 7

Module 7: Exponents and Logarithms

 

In Try This 2 you practised writing exponents as logarithms and practised writing logarithms as exponents for bases other than 10. You may have noticed that the base of an exponent was the same as the base of the logarithm.

 

Did You Know?

Logarithms were invented independently by John Napier and Joost Bürgi in the early 1600s. Both used logarithms to help simplify multiplication and division. Pocket calculators have made this function obsolete; however, logarithms are still useful when solving exponential equations.

 

 

This is a picture of John Napier.

© Classic Image / Alamy

John Napier invented logarithms.

 

This is a picture of Joost Bürgi.

Joost Bürgi

 




Self-Check 1
  1. If the amplitude of vibrations in an earthquake is 1000, determine the resulting magnitude on the Richter scale. Use both the logarithmic notation, y = log10 x, and the exponential notation, x = 10y, to verify that they are equivalent forms. Answer
  2. Convert log3 81 = 4 to exponential form. Answer
  3. Convert 26 = 64 to logarithmic form. Answer