1. Ch. 8.5 Exponential and Logarithmic Equations

2. Exponential and Logarithmic Equations
ALGEBRA 2 LESSON 8-5
Solve 52x = 16.
52x = 16
log 52x = log 16 Take the common logarithm of each side.
2x log 5 = log 16 Use the power property of logarithms.
x = Divide each side by 2 log 5.
log 16
2 log 5
Use a calculator.
Check: 52x
52(0.8614) 16
8-5

3. Check understanding 1

4. For any positive numbers, M, b, and c, with b ≠ 1, and c ≠ 1,
Change of Base Formula
For any positive numbers, M, b, and c, with b ≠ 1, and c ≠ 1,

5. Exponential and Logarithmic Equations
ALGEBRA 2 LESSON 8-5
Use the Change of Base Formula to evaluate log6 12. Then convert log6 12 to a logarithm in base 3.
log6 12 = Use the Change of Base Formula.
log 12
log 6
1.387 Use a calculator.
1.0792
0.7782
log6 12 = log3 x Write an equation.
log3x Substitute log6 12 =
1.387 Use the Change of Base Formula.
log x
log 3
8-5

6. Exponential and Logarithmic Equations
ALGEBRA 2 LESSON 8-5
(continued)
1.387 • log 3 log x Multiply each side by log 3.
1.387 • log x Use a calculator.
log x Simplify.
x Write in exponential form.
Use a calculator.
The expression log6 12 is approximately equal to , or log
8-5

7. Check understanding 2

8. Exponential and Logarithmic Equations
ALGEBRA 2 LESSON 8-5
Solve 52x = 120.
52x = 120
log5 52x = log5 120 Take the base-5 logarithm of each side.
2x = log5 120 Simplify.
2x = Use the Change of Base Formula.
log 120
log 5
x Use a calculator to solve for x.
8-5

9. Check understanding 3

10. Exponential and Logarithmic Equations
ALGEBRA 2 LESSON 8-5
Solve 43x = 1100 by graphing.
Graph the equations y = 43x and y = 1100.
Find the point of intersection.
The solution is x
8-5

11. Exponential and Logarithmic Equations
ALGEBRA 2 LESSON 8-5
Solve log (2x – 2) = 4.
log (2x – 2) = 4
2x – 2 = 104 Write in exponential form.
2x – 2 = 10000
x = 5001 Solve for x.
log 104 = 4
log 10,
log (2 • 5001 – 2) 4
Check: log (2x – 2)
8-5

12. Exponential and Logarithmic Equations
ALGEBRA 2 LESSON 8-5
Solve 3 log x – log 2 = 5.
3 log x – log 2 = 5 x3 2
Log ( ) = 5 Write as a single logarithm. x3 2
= 105 Write in exponential form.
x3 = 2(100,000) Multiply each side by 2.
x = , or about 3
The solution is , or about 3
8-5

13. Check understanding 6

14. Homework
P. 464 # even