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Tell whether each statement is True or False. 1. (log3 2) (10g3 4) = 10g3 8 4. 10g3 2x2 = log3 2 + 210g3 X 2. 3 log, x2 = 6 log, x 5.1083 2x2 = 2 log3 2x 3. logA (x - 4) = log, x log4 4Evaluate each. 1. log2 9 + log2 32 4. logz - - log3 27 + 2 log2 32 2. log4 64 - 10g3 3 5. 2 log2 32 + log4 256 + 3 log3 81 3. log3 9 + log3 81 - log3 27Journal Writing Write a reflection of what you have learned about logarithmic functions, equations and inequalities in a math journal. Many things in our life operate like an equation or an inequality where certain inputs produce outputs. By investing in friendships, we reap happiness. Through working hard, we achieve success. Can you cite examples in life that appear unequally related? Conventions of Journal Writing [includes the date, references to text or data, and personal thoughts and opinions) Capitalization and Punctuation Effective Written Communication Reflection and Thoughts 4. The writer Jllows the conven tions. The writer makes no mistakes . The writer mmmunicat es thoughts in a clear and organized manner. The writer demonstrate s a deep understandi ng of the topic. 3 The writer follows most of the conventions. The writer makes 1-2 mistakes. The writer understandab 1y communicate s the thought, but the organization of ideas should be improved. The writer demonstrates some understandin gof the topic. 2 The writer follows some of the conventions. The writer makes 3-4 mistakes. The writer communicate s in a somewhat organized manner, but ideas were not very clear. The writer demonstrates minimal understandin g of the topic. 1 The writer does not fallow any eonven tion s. The writer makes more than 4 mistakes. The writer's output shows no organization or consideration at all. The writer demonstrates no understandin g of the topic. Definition Examples Logarithmic Function It is a function of the form f(x) = log x , such that b > f(x) = log; x -4 0 and b # 1. y = log2(2x + 3) Logarithmic Equation It is an equation involving log2 4 = log2 X logarithms. log; x +3 = 2 Logarithmic It is an inequality involving log; x 3/2 Reference 3. f(x) = log2 2x - 5 4. f (x) = 23x-2 Solution: 1 . logan + 3 =2 - This is a logarithmic equation because it is an equation involving logarithms. 2. log4 x > 3/2 This is a logarithmic inequality because it is an inequality involving logarithms. 3. f(x) = log2 2x - 5 * This is a logarithmic function because It is a function of the form f(x) = logbx , with b = 2. 4. f(x) = 23x-2 This is neither a logarithmic function, equation, nor inequality because it is an exponential function