Solving Exponential and Logarithmic Equations

Problem: 1

Solve log ₅ 40 = y and check the solution.

Problem: 3

Simplify.

log₁₄36

Problem: 5

Evaluate the logarithm using the change of base formula.

log₆ 320

Problem: 7

Check if x = e⁹ is a solution of the equation:

ln x = 9

Problem: 9

Check if x = ln 2 is a solution of the equation:

4e^x = 8

Problem: 11

Solve the equation.

5^x = 625

Problem: 13

Solve for x.

8e^–x = 4

Problem: 15

Solve:

3^x = 10

Problem: 17

Solve for x.

7^x = 35

Problem: 19

Solve for x.

5^x – 6 = 4

Problem: 21

Solve for x:

Problem: 23

Solve for x.

4(2)^3x – 3 = 12

Problem: 25

Solve the equation.

Problem: 27

Solve for x:

7^x = 3^x

Problem: 29

Solve:

10^x^{– 4} = 100^{3x – 7}

Problem: 31

Solve for x:

2^5x–2 = 5^2x+1

Problem: 33

Solve for x.

Problem: 35

Solve the equation. Check your solution.

Problem: 37

Solve the equation. Check your solution.

22^x^{+ 2}= 57

Problem: 39

Solve the equation. Check your solution.

Problem: 41

Solve:

ln x = 5

Problem: 43

Solve 3 log₂ x = 15.

And check for extraneous solutions.

Problem: 45

Solve:

log₁₀ 3x = 1.5

Problem: 47

Solve the logarithmic equation.

3 log 2x = –2

Problem: 49

Solve the logarithmic equation.

log x – log 4 = 4

Problem: 51

Solve the logarithmic equation.

2 log x – log 5 + log 3.2 = 12

Problem: 53

Solve ln (5 x + 1) = ln (3 x + 7).

And check for extraneous solutions.

Problem: 55

Solve ln x + ln (x – 1) = 1, and check for extraneous solutions.

Problem: 57

Solve ln₆ (13 – 5x) = ln₆ (1 – x).

And check for extraneous solutions.

Problem: 59

In order to double the investment in 5 years, at what rate of compound interest should the money be invested? Solve using common logarithms.

Problem: 61

Consider the following model, N = N₀e^2t, where N₀ is the initial number of particular species in a region and t is the time taken in years. How long will it take to triple in size?

Problem: 63

Lauren deposited $ 800 in a bank that gives an annual interest of 6%. How long will it take for the deposit to reach $1500, if compounded continuously?

Use the formula for continuous compounding : A = Pe^rt

Problem: 1

Solve log ₅ 40 = y and check the solution.

Problem: 3

Simplify.

log₁₄36

Problem: 5

Evaluate the logarithm using the change of base formula.

log₆ 320

Problem: 7

Check if x = e⁹ is a solution of the equation:

ln x = 9

Problem: 9

Check if x = ln 2 is a solution of the equation:

4e^x = 8

Problem: 11

Solve the equation.

5^x = 625

Problem: 13

Solve for x.

8e^–x = 4

Problem: 15

Solve:

3^x = 10

Problem: 17

Solve for x.

7^x = 35

Problem: 19

Solve for x.

5^x – 6 = 4

Problem: 21

Solve for x:

Problem: 23

Solve for x.

4(2)^3x – 3 = 12

Problem: 25

Solve the equation.

Problem: 27

Solve for x:

7^x = 3^x

Problem: 29

Solve:

10^x^{– 4} = 100^{3x
– 7}

Problem: 31

Solve for x:

2^5x–2 = 5^{2x+ 1}

Problem: 33

Solve for x.

Problem: 35

Solve the equation. Check your solution.

Problem: 37

Solve the equation. Check your solution.

22^x^{+ 2}= 57

Problem: 39

Solve the equation. Check your solution.

Problem: 41

Solve:

ln x = 5

Problem: 43

Solve 3 log₂ x = 15.

And check for extraneous solutions.

Problem: 45

Solve:

log₁₀ 3x = 1.5

Problem: 47

Solve the logarithmic equation.

3 log 2x = –2

Problem: 49

Solve the logarithmic equation.

log x – log 4 = 4

Problem: 51

Solve the logarithmic equation.

2 log x – log 5 + log 3.2 = 12

Problem: 53

Solve ln (5x + 1) = ln (3x + 7).

And check for extraneous solutions.

Problem: 55

Solve ln x + ln (x – 1) = 1, and check for extraneous solutions.

Problem: 57

Solve ln₆ (13 – 5x) = ln₆ (1 – x).

And check for extraneous solutions.

Problem: 59

In order to double the investment in 5 years, at what rate of compound interest should the money be invested? Solve using common logarithms.

Problem: 61

Consider the following model, N = N₀e^2t, where N₀ is the initial number of particular species in a region and t is the time taken in years. How long will it take to triple in size?

Problem: 63

Lauren deposited $ 800 in a bank that gives an annual interest of 6%. How long will it take for the deposit to reach $1500, if compounded continuously?

Use the formula for continuous compounding : A = Pe^rt

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