8.3-4 – Logarithmic Functions. Logarithm Functions.

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Presentation transcript:

8.3-4 – Logarithmic Functions

Logarithm Functions

If log b x = y,

Logarithm Functions If log b x = y, then b y = x.

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y b y = x

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y b y = x 8 0 = 1

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 log b x = y b y = x 8 0 = 1

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y b y = x 8 0 = 1

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a = 1000b. 27 ⅓ = 3

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a = 1000b. 27 ⅓ = 3 b y = x

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a = 1000b. 27 ⅓ = 3 b y = x

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a = 1000b. 27 ⅓ = 3 b y = x log b x = y

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a = 1000b. 27 ⅓ = 3 b y = x log b x = y log = 3

Logarithm Functions If log b x = y, then b y = x. Ex. 1 Write the following in exponential form. a. log 8 1 = 0 b. log 2 (1/16) = -4 log b x = y 2 -4 = 1/16 b y = x 8 0 = 1 Ex. 2 Write the following in logarithmic form. a = 1000b. 27 ⅓ = 3 b y = x log 27 3 = ⅓ log b x = y log = 3

Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4

Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y

Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y

Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y b y = x

Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y b y = x 2 y = 64

Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y b y = x 2 y = 64 2 y = 2 6

Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y b y = x 2 y = 64 2 y = 2 6 y = 6

Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log b x = y b y = x 2 y = 64 2 y = 2 6 y = 6

Ex. 3 Evaluate each expression. a. log 2 64 b. log 16 4 log 2 64 = y log 16 4 = y log b x = y 16 y = 4 b y = x (4 2 ) y = 4 2 y = y = y = 2 6 2y = 1 y = 6 y = ½

Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2

Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y

Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b y = x

Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b y = x 9 2 = x

Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b y = x 9 2 = x 81 = x

Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b y = x 9 2 = x 81 = x

Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b 2 = 121 b y = x b = ± = x 81 = x

Ex. 4 Solve each equation. a. log 9 x = 2b. log b 121 = 2 log b x = y b 2 = 121 b y = x b = ± = x b = = x *b cannot be neg.!