Logarithmic Equations Date Period

Kuta Software - Infinite Algebra 2

Logarithmic Equations

Solve each equation.

1) log 5x = log (2x + 9)

3) log (4 p - 2) = log (-5 p + 5)

Name___________________________________ Date________________ Period____

2) log (10 - 4x) = log (10 - 3x)

4) log (4k - 5) = log (2k - 1)

5) log (-2a + 9) = log (7 - 4a)

6) 2 log 7 -2r = 0

7) -10 + log 3 (n + 3) = -10

8) -2 log 5 7x = 2

9) log -m + 2 = 4

10) -6 log 3 (x - 3) = -24

11) log 12 (v2 + 35) = log 12 (-12v - 1)

12) log 9 (-11x + 2) = log 9 (x2 + 30)

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Worksheet by Kuta Software LLC

13) log (16 + 2b) = log (b2 - 4b)

14) ln (n2 + 12) = ln (-9n - 2)

15) log x + log 8 = 2

16) log x - log 2 = 1

17) log 2 + log x = 1

18) log x + log 7 = log 37

19) log 8 2 + log 8 4x2 = 1

20) log 9 (x + 6) - log 9 x = log 9 2

21) log 6 (x + 1) - log 6 x = log 6 29

22) log 5 6 + log 5 2x2 = log 5 48

23) ln 2 - ln (3x + 2) = 1 25) ln (x - 3) - ln (x - 5) = ln 5

24) ln (-3x - 1) - ln 7 = 2 26) ln (4x + 1) - ln 3 = 5

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2

Logarithmic Equations

Solve each equation.

1) log 5x = log (2x + 9) {3}

Name___________________________________ Date________________ Period____

2) log (10 - 4x) = log (10 - 3x) {0}

3) log (4 p - 2) = log (-5 p + 5)

{

7 9

}

5) log (-2a + 9) = log (7 - 4a) {-1}

7) -10 + log 3 (n + 3) = -10 {-2}

9) log -m + 2 = 4

{-100}

4) log (4k - 5) = log (2k - 1) {2}

6) 2 log 7 -2r = 0

{ }1 - 2

8) -2 log 5 7x = 2

{ }1 35

10) -6 log 3 (x - 3) = -24 {84}

11) log 12 (v2 + 35) = log 12 (-12v - 1) {-6}

12) log 9 (-11x + 2) = log 9 (x2 + 30) {-7, -4}

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Worksheet by Kuta Software LLC

13) log (16 + 2b) = log (b2 - 4b) {8, -2}

14) ln (n2 + 12) = ln (-9n - 2) {-2, -7}

15) log x + log 8 = 2

{ }25 2

17) log 2 + log x = 1

{5}

19) log 8 2 + log 8 4x2 = 1

{1, -1}

16) log x - log 2 = 1

{20}

18) log x + log 7 = log 37

{ }37 7

20) log 9 (x + 6) - log 9 x = log 9 2 {6}

21) log 6 (x + 1) - log 6 x = log 6 29

{ }1 28

22) log 5 6 + log 5 2x2 = log 5 48

{2, -2}

23) ln 2 - ln (3x + 2) = 1

{ } 2 - 2 e 3 e

24) ln (-3x - 1) - ln 7 = 2

{ } -7e2 - 1 3

25) ln (x - 3) - ln (x - 5) = ln 5

{ }11 2

26) ln (4x + 1) - ln 3 = 5

{ } 3e5 - 1 4

Create your own worksheets like this one with Infinite Algebra 2. Free trial available at

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