how do we solve exponential and logarithmic equations and equalities?
DESCRIPTION
Equations with logarithms on both sides of the equal sign. A logarithmic equation is an equation with a logarithmic expression that contains a variable. There are two kinds of logarithmic equations: Equations with logarithms on both sides of the equal sign. Equations with logarithms only on one side. (exponentiate the equation) Check answer to make sure it does not give a log(x < 0).TRANSCRIPT
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