5.7 – Exponential Equations

5.7 Exponential Equations

Objectives: I will be able to… Solve Exponential Equations using the

Change of Base Formula

Vocabulary: logarithms, natural logarithms

Daily Objectives

•Perform the Change of Base formula.•Master solving tricky logarithm

equations.▫Exponent variables

Topic One: Change of Base Formula

The BASE goes to the BOTTOM

We typically use log base 10 so we can solve on our calculator!

Example 1: Using Change of Base Formula

2. = 3

3. log 1000

¿𝟏 .𝟐𝟗𝟐

¿𝟑

¿𝟑

This is a great problems to

use the change of

base formula on – Why?

On the other hand, why is

problem #2 not

the type of

problem that you should use the change of base formula

on?

#3 can work with either –

Why?

Example 2: Using Change of Base Formula

Example 1: Solve for a variable exponent when you can have same base

Example 2: Solve for a variable exponent when it’s impossible to get same base

15𝑥=91. Get the base/exponent by itself on one side of the equation

(use PEMDAS)2. Take the log of both sides3. Bring down the exponent via the Log Power Rule4. Get x by itself using Change of Base Rule!5. **Remember: ln(e)=1 and log(10)=1

Example 3: Solve for a variable exponent

Example 4: Solve for a variable exponent

Example 5: Solve for a variable exponent

Example 6: Solve for a variable exponent

Going back to Growth/Decay….

Now we can solve for missing time!In 1990, there were about 5.4 billion people in the world. If the population has been growing at 1.95% per year, estimate the year when the population will be 8 billion people.

Now you solve for time!

Suppose you invest $100 dollars at an annual rate of 6% compounded daily. How long does it take to increase your investment to $150?

Homework

•p. 205 #5-14