5-7

5-7 Exponential Equations

In this lesson, we learned how to solve for an exponent that is a variable. There are two rules:

1. Take the log or ln of both sides. Use ln when the number is e.
2. Put into your calculator only if asked to. Exact values do not get input into a calculator.

Example 1: Solve the equation by using logarithms.

a) 4^x = 20 (take the log of each side of the equation)

= xlog4 = log20 (divide log20 by log4)

= 2.16

b) 25^x = 2 (take the log of each side)

= xlog25 = log2 (divide log2 by log25)

= .22

Example 2: Solve the equation by using logarithms.

- 4^x = 16(sq root of 2) (take the log of each side)

= xlog4 = log16(2)^1/2 (multiply 16 by 2^1/2)

= xlog4 = log22.63 (divide log22.63 by log4)

= 2.25