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**Sec 4.3 Laws of Logarithms Objective:**

To understand the laws of logarithms, including the change of base formula.

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**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:

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**The logarithm of a product of numbers is the sum of the logarithms of the numbers.**

Ex. 1 Evaluate

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**The logarithm of a quotient of numbers is the difference of the logarithms of the numbers.**

Ex. 2 Evaluate

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**The logarithm of a power of a number is the exponent times the logarithm of the number.**

Ex. 3 Evaluate

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**Expanding and Combining Logarithmic Expressions**

Ex 4. Use the Laws of Logarithms to expand each expression.

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**Ex 5. Combine the following into a single logarithm.**

3 log x + ½ log(x + 1)

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**Ex 6. Combing the following into a single logarithm.**

3 ln s + ½ ln t – 4 ln(t2 + 1)

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Change of Base

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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

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**Solving an Exponential Equation**

Ex 8. Solve for x. Round to 3 decimal places.

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

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

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HW – Log Worksheet

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