Holt McDougal Algebra 2

Exponential and Logarithmic Equations and InequalitiesExponential and Logarithmic Equations and Inequalities

Holt Algebra 2Holt McDougal Algebra 2

• How do we solve exponential and logarithmic equations and equalities?

• How do we solve problems involving exponential and logarithmic equations?

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

• Equations with logarithms on both sides of the equal sign.

• Equations with logarithms only on one side. (exponentiate the equation)

A logarithmic equation is an equation with a logarithmic expression that contains a variable. There are two kinds of logarithmic equations:

17log then ,17log If bbx xb

b 17 :meansWhich bx

Check answer to make sure it does not give a log(x < 0).

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

13 log3 log .1 xx

133 xx

Solve the equation.

2

1x

Solving Logarithmic Equations

x x 11x2

2 2

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

114ln 4ln .2 xx1144 xx

Solve the equation.

15

3x

Solving Logarithmic Equations

x x 1111x5

5 5

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

7 log2log229 log .3 777 xx

74

29

xx

Solve the equation.

x5

6x

Solving Logarithmic Equations

x4x4 2 230

5 5

2

429log7

x 7log7 x

29 x 284 x1

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

5log232 log2log33 log .4 3333 xx

2532

83

xx

Solve the equation.

x9

11x

Solving Logarithmic Equations

x16x16 75 7599

9 9

3

83log3

x

25

32log3x

7525 x 2416 x

2

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

Solve the equation.Solving Logarithmic Equations

327 log .5 4 x

327log 44 4 x

27x

37x

6427 27

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

Solve the equation.Solving Logarithmic Equations

25 log .6 38 x

3/25log 88 8 x

5x

9x

45 5

5log8 x

33 3

32

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

Solve the equation.Solving Logarithmic Equations

1152 log 3 .7 5 x

22log 55 5 x

23x2 2

5 5

2log3 5 x 63 3 2log5 x 2

2x 25

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

Solve the equation.Solving Logarithmic Equations

52ln 4 .8 x

4/52ln ee x x2

74.1x

49.3

4 4

x2ln45

2 2

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

Solve the equation.Solving Logarithmic Equations

1173001ln 10 .9 x

55.1627x100 100

12100ln ee x

3 3

x100ln10 12010 10

x100ln 12

x100 79.754,162

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

10. The moment magnitude M of an earthquake that releases energy E (in ergs) can be modeled by this equation:

Economics Application

Substitute 4.2 for M.4.2 = 0.219ln E +1.17Solve for E.

17.1ln219.0 EMOn October 9, 1984, the largest earthquake in Georgia occurred in Dalton with a magnitude of 4.2. How much energy did this earthquake release?

17.117.103.3 Eln219.0

219.0 219.0836.13 Eln

836.13ln ee E 309,020,1E

The earthquake released about 1,020,309 ergs of energy.

Holt McDougal Algebra 2

Exponential and Logarithmic Equations and Inequalities

Lesson 9.2 Practice B