Worksheet Key 4/16/2019 10:25 PM 5.4 - Common Logarithms

Expanding and Condensing Logarithms Section 5.4 Pre-Calculus AB PreAP, Revised ©2015 viet.dang@humble.k12.tx.us 4/16/2019 10:25 PM 5.4 - Common Logarithms

7.5 - Properties of Logarithms Review Exponent Rules A. Product: B. Quotient: C. Power: n + m n – m n* m 4/16/2019 10:25 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Log Properties A. Product: B. Quotient: C. Power: 4/16/2019 10:25 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Expanding Logarithms A. Expanding Logarithms involves breaking down a simpler component into a complicated expression. The answer will involve more than one logarithm. B. Condensing Logarithms involves breaking down a complicated expression into simpler components. The answer will involve ONLY one logarithm. 4/16/2019 10:25 PM 7.5 - Properties of Logarithms

7.5 - Properties of Logarithms Review Expand log (ab) 4/16/2019 10:25 PM 7.5 - Properties of Logarithms

5.5 - Properties of Logarithms Example 1 Using 𝐥𝐨𝐠𝟕≈𝟎.𝟖𝟒𝟓𝟏 𝐥𝐨𝐠𝟗≈𝟎.𝟗𝟓𝟒𝟐 , approximate log 63 4/16/2019 10:25 PM 5.5 - Properties of Logarithms

5.5 - Properties of Logarithms Example 2 Using 𝐥𝐨𝐠𝟕≈𝟎.𝟖𝟒𝟓𝟏 𝐥𝐨𝐠𝟗≈𝟎.𝟗𝟓𝟒𝟐 , approximate log 9/7 4/16/2019 10:25 PM 5.5 - Properties of Logarithms

5.5 - Properties of Logarithms Example 3 Using 𝐥𝐨𝐠𝟕≈𝟎.𝟖𝟒𝟓𝟏 𝐥𝐨𝐠𝟗≈𝟎.𝟗𝟓𝟒𝟐 , approximate log 81 4/16/2019 10:25 PM 5.5 - Properties of Logarithms

5.5 - Properties of Logarithms Your Turn Using 𝐥𝐨𝐠𝟕≈𝟎.𝟖𝟒𝟓𝟏 𝐥𝐨𝐠𝟗≈𝟎.𝟗𝟓𝟒𝟐 , approximate log 81/49 4/16/2019 10:25 PM 5.5 - Properties of Logarithms

We’ll answer that question later… 5.3 - Properties of Logarithms Review Review: What’s 23 and 24 = ? Answer: 8 and 16 because its 2 · 2 · 2 = 8 and 2 · 2 · 2 · 2 = 16. So we know that 23 = 8 and 24 = 16. However, what is 2x = 10? We’ll answer that question later… 4/16/2019 10:25 PM 5.3 - Properties of Logarithms

5.3 - Properties of Logarithms Change of Base Change of Base Formula: 𝐥𝐨𝐠 𝐛 𝒙= 𝐥𝐨𝐠 𝒙 𝐥𝐨𝐠 𝒃 We use this formula when we need to solve for x Remember the question, 2x = 10? 4/16/2019 10:25 PM 5.3 - Properties of Logarithms

5.3 - Properties of Logarithms Change of Base 4/16/2019 10:25 PM 5.3 - Properties of Logarithms

Example 4 Solve for x, 2x = 10 We will need to use calculators to figure this out. 4/16/2019 10:25 PM 5.3 - Properties of Logarithms

5.3 - Properties of Logarithms Example 4 Solve for x, 2x = 10 4/16/2019 10:25 PM 5.3 - Properties of Logarithms

5.3 - Properties of Logarithms Example 5 Evaluate log26 4/16/2019 10:25 PM 5.3 - Properties of Logarithms

5.3 - Properties of Logarithms Example 6 Evaluate 𝐥𝐨𝐠 𝟔 𝟔 4/16/2019 10:25 PM 5.3 - Properties of Logarithms

5.3 - Properties of Logarithms Your Turn Evaluate 𝐥𝐨𝐠 𝟔 𝟔 4/16/2019 10:25 PM 5.3 - Properties of Logarithms

Example 7 Simplify log552+x without a calculator 4/16/2019 10:25 PM 5.4 - Common Logarithms

Example 8 Simplify log 10x2 + y2 without a calculator 4/16/2019 10:25 PM 5.4 - Common Logarithms

Your Turn Evaluate log010 4/16/2019 10:25 PM 5.4 - Common Logarithms

Example 9 The population of a coastal town currently holds 3,400 and grows at a rate of 3% per year. The growth can be expressed by the exponential equation P = 3400(1 + 0.03)t, where P is the population after t years. Find the number of years it will take for the population to have at least 5,000 people. Round answer to the 3 decimal places. 4/16/2019 10:25 PM 5.4 - Common Logarithms

Example 9 The population of a coastal town currently holds 3,400 and grows at a rate of 3% per year. The growth can be expressed by the exponential equation P = 3400(1 + 0.03)t, where P is the population after t years. Find the number of years it will take for the population to have at least 5,000 people. Round answer to the 3 decimal places. 4/16/2019 10:25 PM 5.4 - Common Logarithms

Your Turn The population of Wahoo, Nebraska is declining at a rate of 7% per year. The decline can be expressed by the exponential equation P = C(1 – 0.07)t where P is the population after t years and C is the current population. If the population was 8,500 in 2004, when will the population be less than 6,000? Round answer to the nearest whole number 4/16/2019 10:25 PM 5.4 - Common Logarithms

Assignment Worksheet 4/16/2019 10:25 PM 5.4 - Common Logarithms