Warm-Up

Find the inverse of each function.

1) f(x) = x + 10

2) g(x) = 3x

3) h(x) = 5x + 3

4) j(x) = ¼x + 2

6.3 Logarithmic Functions

6.3 Logarithmic Functions

• Write equivalent forms for exponential and logarithmic equations.

• Use the definitions of exponential and logarithmic functions to solve equations.

6.3 Logarithmic Functions

Rules and Properties

Equivalent Exponential and Logarithmic Forms

310 1000

bx = y if and only if x = logb y.

6.3 Logarithmic Functions

For any positive base b, where b 1:

Exponential form Logarithmic form

10 1log 000 3

Example 1

a) Write 27 = 128 in logarithmic form.

6.3 Logarithmic Functions

log2 128 = 7

b) Write log6 1296 = 4 in exponential form.

64 = 1296

Example 2

x = 3

2x = 8

6.3 Logarithmic Functions

a. Solve x = log2 8 for x.

x = 5

x2 = 25

b. logx 25 = 2

Practice

x = 16

24 = x

6.3 Logarithmic Functions

c. Solve log2 x = 4 for x.

Example 3

x = 1.161

log1014.5 = x

6.3 Logarithmic Functions

a. Solve 10x = 14.5 for x. Round your answer to the nearest tenth.

Rules and Properties

logb xb xlog x

b b x

log 1 0b

6.3 Logarithmic Functions

If bx = by, then x = y.

log 1b b

Example 4

a) log2 1 = r

6.3 Logarithmic Functions

Find the value of the variable in each equation:

2r = 1

20 = 1r = 0

Simplify the expression

a)2log 2x

x

7log 37 xb)

3x

Practice

1) log4 64 = v

6.3 Logarithmic Functions

Find the value of the variable in each equation:

2) logv 25 = 2

3) 6 = log3 v

V=3

V=5

V=729

p.436 #30-68 ev

Homework6.3 Logarithmic Functions