 # Quiz 3.2. 3.3 Properties of Logarithms Date: ____________.

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Quiz 3.2

3.3 Properties of Logarithms Date: ____________

Change of Base Theorem log a x= log x log a log a x= ln x ln a OR

1) 2)

1) 2)

Evaluating Logarithms log 5 23= log23 log5 ≈ 1.948 OR log 5 23= ln23 ln5 ≈ 1.948

Other Examples log 3 149= log149 log3 ≈ 4.555 log 7 300= log300 log7 ≈ 2.9312

Properties of Logarithms Product Property Quotient Property Power Property Let b, u, and v be positive numbers such that b ≠ 1. log b uv = log b u + log b v log b u n = nlog b u log b = log b u − log b v u v

1) 2) 3)

1) 2) 3)

Find the exact value of the logarithm.

Use the properties of logarithms to simplify the given expression.

Write as the sum, difference, or product of logarithms. Simplify, if possible. log 4 4x64x6 y =log 4 4x 6 – log 4 y = log 4 4 + log 4 x 6 – log 4 y = log 4 4 + 6log 4 x – log 4 y = 1 + 6log 4 x – log 4 y

Write as the sum, difference, or product of logarithms. Simplify, if possible. log 7 6 x3yx3y =log 7 6 – log 7 x 3 y = log 7 6 −(log 7 x 3 + log 7 y) = log 7 6 − (3log 7 x + log 7 y) = log 7 6 − 3log 7 x − log 7 y

Write as the sum, difference, or product of logarithms. Simplify, if possible. log 5 7 x= log 5 7 + log 5 x = log 5 7 + log 5 x ½ = log 5 7 + ½log 5 x

Write as the sum, difference, or product of logarithms. Simplify, if possible. log a x3y5x3y5 z = log a x3y5x3y5 z ½ = ½ log a x3y5x3y5 z = ½( log a x 3 + log a y 5 – log a z) = ½(3 log a x+ 5log a y – log a z)

Condense the expression to the logarithm of a single quantity. log 3 5 + 6log 3 x − log 3 7 = log 3 5 + log 3 x 6 − log 3 7 = log 3 (5x 6 ) − log 3 7 = log 3 7 5x 6

Condense the expression to the logarithm of a single quantity. 3log 8 x − 5log 8 y + log 8 15 = log 8 x 3 − log 8 y 5 + log 8 15 15 log 8 y5y5 = x3x3 = log 8 y5y5 15x 3

x3x3 Condense the expression to the logarithm of a single quantity. 3log 8 x − 5log 8 y − log 8 15 = log 8 x 3 − log 8 y 5 − log 8 15 = log 8 15y 5