Math Worksheets Name: __________
Date: ___________
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Solving Logarithmic Equations
Find the value of the variables in each equation.
1) 2πππ 7 β 2π₯ = 0
2) βπππ 5 7π₯ = 2
3) log π₯ + 5 = 2
4) πππ π₯ β πππ 4 = 3
5) πππ π₯ + πππ 2 = 4
6) πππ 10 + πππ π₯ = 1
7) πππ π₯ + πππ 8 = πππ 48
8) β3 πππ 3(π₯ β 2) = β12
9) πππ 6π₯ = πππ (π₯ + 5)
10) πππ (4π β 5) = πππ (2π β 1)
11) πππ(4π β 2) = πππ(β5π + 5)
12) β10 + πππ 3 (π + 3) = β10
13) πππ 9(π₯ + 2) = πππ 9 (π₯2 + 30)
14) πππ 12 (π£2 + 35) = πππ 12 (β2π£ β 1)
15) πππ (16 + 2π) = πππ (π2 β 4π)
16) πππ 9(π₯ + 6) β πππ 9 π₯ = πππ 9 2
17) πππ 56 + πππ 5 2π₯2 = πππ 5 48
18) πππ 6(π₯ + 1) β πππ 6 π₯ = πππ 6 29
Find the value of x in each natural logarithm equation.
19) ππ 2 β ππ(3π₯ + 2) = 1
20) ππ(π₯ β 3) β ππ(π₯ β 5) = ππ 5
21) ππ π4 β ππ(π₯ + 1) = 1
22) ππ(2π₯ β 1) β ππ(π₯ β 5) = ππ 5
23) ππ 2π₯ + ππ(3π₯ β 4) = ln 4π₯
24) ππ(4π₯ β 2) β 4ππ(π₯ β 5) = ππ 10
25) ππ (4π₯ + 2) β ππ 1 = 5
26) ππ(π₯ β 3) + ππ(π₯ β 5) = ππ 2
27) ππ 2 + ππ(3π₯ + 2) = 4
28) 2 ππ 4π₯ β ππ(π₯ + 6) = 2 ππ 3π₯
29) ππ π₯2 + ππ π₯3 = ππ 1
30) ππ π₯4 β ππ(π₯ + 4) = 4 ππ π₯
31) 2 ππ(π₯ β 3) = ππ(π₯2 β 6π₯ + 9)
32) ππ(π₯2 + 12) = ππ(6π₯ + 4)
33) 2 ππ π₯ β 2ππ(π₯ + 2) = 4ππ(π₯2)
34) ππ(4π₯ β 3) β ππ(2π₯ β 4) = ππ 5
35) ππ 2 + 4 ππ(π₯ + 2) = ππ 2
36) 2ππ π2 + ππ(2π₯ β 1) = ππ 5 + 4
Math Worksheets Name: __________
Date: ___________
β¦ So Much More Online! Please visit: www.EffortlessMath.com
Answers
Solving Logarithmic Equations
1) {β1
2}
2) {1
175}
3) {β1
1,000}
4) {4,000}
5) {5,000}
6) {1}
7) {6}
8) {83}
9) {1}
10) {2}
11) {7
9}
12) {β2}
13) No Solution
14) No Solution
15) {8, β2}
16) {6}
17) {β3, ββ3}
18) {1
28}
19) π₯ =2β2π
3π= β0.42
20) {11
2}
21) π3 β 1
22) {8}
23) {2}
24) {6.23}
25) π₯ =π5β2
4
26) π₯ = 4 + β3
27) π₯ =π4β4
6
28) No Solution
29) {1}
30) No Solution
31) π₯ > 3
32) {2, 4}
33) {0.71667 β¦ }
34) {17
6}
35) {β1}
36) {3}