University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

121

Pages:

3
Author:

karencillaki50

6.3 Logarithms and Logarithmic Functions Section A: Vocabulary & Concepts Logarithm of y with base b. logb y = x if and only if b^x = y Example: log2 8 = 3 because 2^3 = 8 Common Logarithm log x = log10 x Base 10 Natural Logarithm loge x = ln x Base e Graphs of Logarithms Tables of values for y = 2^x and y = log2 x Graph of y = 2^x and its reflection over the line y = x, which is the graph of y = log2 x. Observation: "The domain and range are switched (x, y) → (y, x)." "The exponential function is reflected over y = x." "LOGARITHMS ARE THE INVERSE OF EXPONENTIAL FUNCTIONS!" 1. Rewrite the equation in exponential form. a. log₂ 16 = 4 2⁴ = 16 b. log₄ 1 = 0 4⁰ = 1 c. log₁₂ 12 = 1 12¹ = 12 d. log₁/₄ 4 = -1 (¼)-¹ = 4 2. Rewrite each equation in logarithmic form a. 5² = 25 log₅ 25 = 2 b. 10⁻¹ = 0.1 log₁₀ 0.1 = -1 c. 6⁻³ = 1/216 log₆ (1/216) = -3 d. 8²/³ = 4 log₈ 4 = 2/3 3. Evaluate each logarithm a. log₄ 64 3 (because 4³ = 64) b. log₅ 0.2 -1 (because 5⁻¹ = 0.2) c. log₁/₅ 125 -3 (because (1/5)⁻³ = 125) d. log₁/₂ 36 -2 (because (1/2)⁻² = 36) Evaluating common and Natural Logarithms Instructions: Use a calculator a. log 8 ≈ 0.903 b. log 12 ≈ 1.079 c. ln 0.3 ≈ -1.204 d. ln 0.75 - 0.288 Title: 5. Simplify Inverse Properties logb x = x b^(logb x) = x a. 10^(log4) = 4 b. log5 25^x = 2x c. log3 27^(2x) = 6x Title: 6. Find the inverse. a. f(x) = 6^x Step 1: Switch x and y: x = 6^y Step 2: Solve for y: y = log6 x Inverse: f^(-1)(x) = log6 x