Example 1 LOGARITHMIC FORM EXPONENTIAL FORM a. log2 16 = 4 24 = 16 b.

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Example 1 LOGARITHMIC FORM EXPONENTIAL FORM a. log2 16 = 4 24 = 16 b. Rewrite Logarithmic Equations LOGARITHMIC FORM EXPONENTIAL FORM a. log2 16 = 4 24 = 16 b. log7 1 = 70 = 1 c. log5 5 = 1 51 = 5 d. log 0.01 = 2 – = 0.01 10 2 – = 4 1 – e. log1/4 4 = 1 –

Rewrite the equation in exponential form. Checkpoint Rewrite Logarithmic Equations Rewrite the equation in exponential form. 1. log3 81 = 4 ANSWER 34 = 81 2. log4 4 = 1 41 = 4 ANSWER 3. log6 1 = 60 = 1 ANSWER = 4 2 1 – ANSWER log1/2 4 4. = 2 –

Evaluate the expression. Example 2 Evaluate Logarithmic Expressions Evaluate the expression. a. log4 64 b. log4 2 c. log1/3 9 SOLUTION To help you find the value of logb y, ask yourself what power of b gives you y. a. 4? = 64 What power of 4 gives 64? 43 = 64 Guess, check, and revise. Definition of logb y log4 64 = 3 3

Example 2 Evaluate Logarithmic Expressions b. 4? = 2 What power of 4 gives 2? 41/2 = 2 Guess, check, and revise. Definition of logb y log4 2 = 2 1 c. = 9 3 1 What power of gives 9? ? = 9 3 1 – 2 Guess, check, and revise. log1/3 9 = 2 – Definition of logb y 4

Example 3 a. Evaluate 10log 6. b. Simplify log2 8x. SOLUTION Use Inverse Properties a. Evaluate 10log 6. b. Simplify log2 8x. SOLUTION a. 10log 6 = 10 log10 6 6 = b. log2 8x = log2 x ( ) 23 = log2 23x = 3x 5

Checkpoint 5. Evaluate log2 64. 6 ANSWER 6. Evaluate log4 16 1 . Evaluate and Simplify Logarithmic Expressions 5. Evaluate log2 64. 6 ANSWER 6. Evaluate log4 16 1 . ANSWER 2 – ANSWER 2 1 7. Evaluate log16 4. 8. Simplify 7 . log7 x x ANSWER 9. Simplify log5 25x. 2x ANSWER

Checkpoint 6x 10. Simplify log2 64x. ANSWER Evaluate and Simplify Logarithmic Expressions 10. Simplify log2 64x. 6x ANSWER

For both graphs, find the two key points where and where = y 1. Example 4 Graph Logarithmic Functions Graph the function. Describe the vertical asymptote. State the domain and range. a. y = log3 x b. y = log3 ( x – 2 ) SOLUTION For both graphs, find the two key points where and where = y 1. Let Then , so is on the graph. = x 1. y log3 1 ( ) 1, 0 Let Then , so is on the graph. = x 3. y log3 3 1 ( ) 3, 1 8

Example 4 Graph Logarithmic Functions The vertical asymptote is the y-axis. The domain is , and the range is all real numbers. x > b. Let Then , so is on the graph. = x 3. ( ) 3, 0 3 – y log3 2 Let Then so is on the graph. = x 5. ( ) 5, 1 1, 5 – y log3 2 The vertical asymptote is The domain is , and the range is all real numbers. 2 > x = 2. 9

; domain: , range: all real numbers = x > Checkpoint Graph Logarithmic Functions Graph the function. Describe the vertical asymptote. State the domain and range. 11. y = log10 x ANSWER ; domain: , range: all real numbers = x >

; domain: , range: all real numbers = x 3 > Checkpoint Graph Logarithmic Functions Graph the function. Describe the vertical asymptote. State the domain and range. 12. x – = y log2 ( ) 3 ANSWER ; domain: , range: all real numbers = x 3 >

; domain: , range: all real numbers = x > Checkpoint Graph Logarithmic Functions Graph the function. Describe the vertical asymptote. State the domain and range. 13. y = log5 x + 3 ANSWER ; domain: , range: all real numbers = x >