Intermediate Algebra (11th edition)

2.If then

To solve logarithmic equations, use these properties, where
First use the properties of
Section 10.4,if necessary, to write the equation in the
proper form.

1.If then

2.If then

Always check proposed solutions in logarithmic equations.

logb x=y, by=x.

logb x=logb y, x=y.

b 7 0, bZ1, x 7 0, y 7 0.

x=y, x 7 0, y 7 0, logb x=logb y. Solve.

Take common logarithms.

Power rule

Divide by log 5.

The solution set is

Solve.

Subtract x.

This value checks, so the solution set is

Solve.

Exponential form

Apply the exponent.

Add 1.

Divide by 3.

This value checks, so the solution set is E^173 F.

x=

17

3

3 x= 17

3 x- 1 = 16

3 x- 1 = 24

log 2 13 x- 12 = 4

516.

x= 1

2 x=x+ 1

log 3 2 x=log 3 1 x+ 12

5 1.2920 6.

m=

log 8

log 5

L1.2920

m log 5=log 8

log 5 m=log 8

5 m= 8

CONCEPTS EXAMPLES

REVIEW EXERCISES

CHAPTER 10

10.1 Determine whether each graph is the graph of a one-to-one function.

1. 2.

0

x

y

0

x

y

626 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions

Determine whether each function is one-to-one. If it is, find its inverse.

3.ƒ 1 x 2 =- 3 x+ 7 4.ƒ 1 x 2 = 236 x- 4 5.ƒ 1 x 2 =-x^2 + 3