1. Sec 4.3 Laws of Logarithms Objective:
To understand the laws of logarithms, including the change of base formula.

2. Laws of Logarithms Let a be a positive number, with a ≠ 1.
Let A, B, and C be any real numbers with A > 0 and B > 0, then the following laws apply:

3. The logarithm of a product of numbers is the sum of the logarithms of the numbers.
Ex. 1 Evaluate

4. The logarithm of a quotient of numbers is the difference of the logarithms of the numbers.
Ex. 2 Evaluate

5. The logarithm of a power of a number is the exponent times the logarithm of the number.
Ex. 3 Evaluate

6. Expanding and Combining Logarithmic Expressions
Ex 4. Use the Laws of Logarithms to expand each expression.

7. Ex 5. Combine the following into a single logarithm.
3 log x + ½ log(x + 1)

8. Ex 6. Combing the following into a single logarithm.
3 ln s + ½ ln t – 4 ln(t2 + 1)

9. Change of Base

10. Ex 7. Use the Change of Base Formula and common or natural logarithms to evaluate each logarithm, correct to five decimal places.
(a) log8 5
(b) log9 20

11. Solving an Exponential Equation
Ex 8. Solve for x. Round to 3 decimal places.

12. Ex. 9 Solve for x. Round to 3 decimal places.

13. Ex 10. Solve for x. Round to 3 decimal places.

14. HW – Log Worksheet