# Sec 4.3 Laws of Logarithms Objective:

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

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:

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

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

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

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

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

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

Change of Base

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

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

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

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

HW – Log Worksheet