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3. log(x) + log(7) = 2 5. 3 log(2x - 1) = 1 Worksheets for Math 05 4. log(x) +5 + 5 = 6.2 6.log(x + 2) + log(5) = 1 Earlier we noted that if m= n, then log(m) = log (n). The converse of the statement is also other words, if log(m) = log (n), then m = n. Although the situation has not arisen in the p examples, we need to check that our answers that determines which value of x is the solutic equation. Logarithms of negative numbers are undefined and not all preliminary answers ar to the original logarithmic equation. These solutions are called extraneous solutions to the equation. Example 7: Solve the equation In(x + 2) + In(x - 2) = In (5).

3. log(x) + log(7) = 2 5. 3 log(2x - 1) = 1 Worksheets for Math 05 4. log(x) +5 + 5 = 6.2 6.log(x + 2) + log(5) = 1 Earlier we noted that if m= n, then log(m) = log (n). The converse of the statement is also other words, if log(m) = log (n), then m = n. Although the situation has not arisen in the p examples, we need to check that our answers that determines which value of x is the solutic equation. Logarithms of negative numbers are undefined and not all preliminary answers ar to the original logarithmic equation. These solutions are called extraneous solutions to the equation. Example 7: Solve the equation In(x + 2) + In(x - 2) = In (5).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 45RE
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3. log(x) + log(7) = 2 - 5. 3 log(2x − 1) = 1 Example 7: Worksheets for Math 096 4. log(x) + 5 = 6.2 6.log(x + 2) + log(5) = 1 2 Earlier we noted that if m= n, then log(m) = log (n). The converse of the statement is also true. In other words, if log(m) = log (n), then m = n. Although the situation has not arisen in the previous examples, we need to check that our answers that determines which value of x is the solution to th equation. Logarithms of negative numbers are undefined and not all preliminary answers are solut to the original logarithmic equation. These solutions are called extraneous solutions to the original equation. Solve the equation In(x + 2) + In(x - 2) = ln (5).
Transcribed Image Text:3. log(x) + log(7) = 2 - 5. 3 log(2x − 1) = 1 Example 7: Worksheets for Math 096 4. log(x) + 5 = 6.2 6.log(x + 2) + log(5) = 1 2 Earlier we noted that if m= n, then log(m) = log (n). The converse of the statement is also true. In other words, if log(m) = log (n), then m = n. Although the situation has not arisen in the previous examples, we need to check that our answers that determines which value of x is the solution to th equation. Logarithms of negative numbers are undefined and not all preliminary answers are solut to the original logarithmic equation. These solutions are called extraneous solutions to the original equation. Solve the equation In(x + 2) + In(x - 2) = ln (5).
Example 5: Step 1: Step 2: Step 3: Example 6: Step 1: Step 2: Step 3: Step 4: Solve the equation log(x) - log (7) = 2. 10g (+)-2 ==10²-100 X=7·100=700 7 Solve the equation log(2x) + log (5) = 3. Problem Set C: Solve and check the following equations: 1. log(3x) + 5 = 6.2 log(C2x) (5))=3 log(10x) = 3 lox=10³ = 1000 X = 1000 10 =100 2. 2 log(3-x) = 1
Transcribed Image Text:Example 5: Step 1: Step 2: Step 3: Example 6: Step 1: Step 2: Step 3: Step 4: Solve the equation log(x) - log (7) = 2. 10g (+)-2 ==10²-100 X=7·100=700 7 Solve the equation log(2x) + log (5) = 3. Problem Set C: Solve and check the following equations: 1. log(3x) + 5 = 6.2 log(C2x) (5))=3 log(10x) = 3 lox=10³ = 1000 X = 1000 10 =100 2. 2 log(3-x) = 1
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