1. Lesson 3

1.3. Explore 2

Mathematics 30-2 Module 7

Module 7: Exponents and Logarithms

 

The patterns you have seen so far allow you to convert between exponents and logarithms.

 

 

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.


In Try This 2 you will convert between logarithmic and exponential form and investigate logarithms with bases other than 10.

 

Try This 2
  1. Complete a table similar to the following for y = log2 x.

    Exponential Form

    x = 10y

    Logarithmic Form

    y = log10 x
    1 = 100 0 = log10 1
    10 = 101 1 = log10 10
    100 = 102 2 = log10 100
    1000 = 103 3 = log10 1000
    10 000 = 104 4 = log10 10 000

    Exponential Form

    x = 2y

    Logarithmic Form

    y = log2 x
    1 = 20 0 = log2 1
    2 = 21
       
       
       
  2. Convert the following expressions into logarithmic form.
    1. 10 000 000 = 107
    2. 64 = 26
    3. 243 = 35
  3. Convert the following expressions into exponential form.
    1. log10 1 000 000 = 6
    2. log2 256 = 8
    3. log17 118 587 876 497 = 9

course folder Save your responses in your course folder.

Use the pattern in the previous table to help you.
1 = log2 2