1. Lesson 3

1.9. Lesson 3 Summary

Mathematics 30-2 Module 7

Module 7: Exponents and Logarithms

 

Lesson 3 Summary

 

In this lesson you learned about evaluating logarithmic expressions and the relationship between logarithmic notation and exponential notation in a variety of contexts.

 

This diagram shows an expression in logarithmic form and in exponential form. In logarithmic form, it is written as the base b logarithm of x is equal to y. In exponential form, b to the power of y is equal to x. The y’s are labelled “exponent” and the b’s are labelled “base.”

Source: Pre-Calculus 12. Whitby, ON: McGraw-Hill Ryerson, 2011.

Reproduced with permission. Reproduced with permission.

 


The logarithmic function y = logb x is equivalent to the exponential expression x = by. The value of a logarithm can be determined by letting the logarithm equal y, converting to exponential form, and then determining y. You cannot take the logarithm of a negative number. Logarithms are especially useful when working with numbers that are very large or very small, or that occur across a very large range.