Lesson 6

Watch Solving Exponential Equations with Two Powers to see how an exponential equation with multiple powers, similar to the one you saw in Try This 2, can be solved.

When working with logarithms, it can be useful to change the base of the logarithm. Some calculators will not accept most bases, so converting to base 10 allows you to determine a decimal approximation. In Try This 3 you will explore a method that can be used to convert between bases.

Try This 3

1. Consider the equation y = log4 20. Complete the following steps to give an expression of y using base-10 logarithms.
   
   

   Write the original logarithm.	y = log4 20
   Rewrite the logarithm in exponential form.
   Take the base-10 logarithm of each side of the equation.
   Use the power law of logarithms, logb (Mn) = n logb M, to “bring down” the exponent y.
   Divide both sides by log 4 to isolate y.

2. Compare the resulting expression with the initial expression in question 1. Describe a rule showing how logb x can be rewritten using a different base.

Save your responses in your course folder.