Properties of Logarithms: An Example-Based Guide

University:
Glendale Community College
Course:
MAT150 | College Algebra/Functions
Academic year:

2020
Views:

85

Pages:

3
Author:

Giselle Travis

Section 6.5: Properties of Logarithms Examples: 𝑙𝑜𝑔2 (8 ∗ 4) = 𝑙𝑜𝑔2 (8) + 𝑙𝑜𝑔2 (4) 𝑙𝑜𝑔3 (9 ∗ 81) = 𝑙𝑜𝑔3 (9) + 𝑙𝑜𝑔3 (81) 𝑙𝑜𝑔7 (𝑥𝑦) = 𝑙𝑜𝑔7 (𝑥) + 𝑙𝑜𝑔7 (𝑦) 𝑙𝑜𝑔5 (125) + 𝑙𝑜𝑔5 (625) = 𝑙𝑜𝑔5 (125 ∗ 625) 𝑙𝑜𝑔5 (𝑦) + 𝑙𝑜𝑔5 (𝑧) = 𝑙𝑜𝑔5 (𝑦𝑧) Examples: 8 𝑙𝑜𝑔2 (4) = 𝑙𝑜𝑔2 (8) − 𝑙𝑜𝑔2 (4) 9 81 𝑙𝑜𝑔3 ( ) = 𝑙𝑜𝑔3 (9) − 𝑙𝑜𝑔3 (81) 𝑥 𝑙𝑜𝑔7 (𝑦) = 𝑙𝑜𝑔7 (𝑥) − 𝑙𝑜𝑔7 (𝑦) 125 𝑙𝑜𝑔5 (125) − 𝑙𝑜𝑔5 (625) = 𝑙𝑜𝑔5 (625) 𝑦 𝑙𝑜𝑔5 (𝑦) − 𝑙𝑜𝑔5 (𝑧) = 𝑙𝑜𝑔5 ( 𝑧 ) Examples: 𝑙𝑜𝑔6 (364 ) = 4𝑙𝑜𝑔6 (36) 𝑙𝑜𝑔9 (812 ) = 2𝑙𝑜𝑔9 (81) 𝑙𝑜𝑔5 (𝑥 7 ) = 7𝑙𝑜𝑔5 (𝑥) 4𝑙𝑜𝑔2 (64) = 𝑙𝑜𝑔2 (644 ) 3𝑙𝑜𝑔𝑏 (𝑥) = 𝑙𝑜𝑔𝑏 (𝑥 3 ) Examples: 𝑙𝑜𝑔3 (1) = 0 ln(1) = 0 log(1) = 0 Examples: 𝑙𝑜𝑔2 (2) = 1 𝑙𝑜𝑔4 (4) = 1 log(10) = 1 ln(𝑒) = 1 Examples: 𝑙𝑜𝑔4 (45 ) = 5 𝑙𝑜𝑔3 (39 ) = 9 𝑙𝑛(𝑒 7 ) = 7 𝑙𝑜𝑔(102 ) = 2 Examples: 3𝑙𝑜𝑔3 (7) = 7 5𝑙𝑜𝑔5 (3) = 3 4𝑙𝑜𝑔4 (𝑥) = 𝑥