- Solving for Exponents Calculator
- Basic Explanation
- In-Depth Explanation
- Solving for Exponents Practice Problems

^ X =

X = 0

X = 0

» Show Work

Enter problem to view work.

basic explanation:

Solving for exponents problems are best solved using logarithms. Our in-depth explanation shows you exactly how to accomplish the task. However, when there are simple solutions, such as when the answer to the exponent problem is equal to 1, X will either equal any real number (if the base is 1) or 0 (if the base isn't 1).

in-depth explanation:

To solve for an unknown exponent, the best solution, as stated earlier, is normally using logarithms. This section will give you a detailed explanation on this method. First, since equation will remain the same if you alter it equally on both sides, you can rewrite the equation by taking the log (logarithm) of both sides: log(A^X) = log(B). In this example, A will be the base, X is the unknown exponent, and B is the answer. Next you may rewrite the equation to X * log(A) = log(B) since the equation remains equivalent. Afterwards, divide both sides by log(A) to make the equation appear like X = log(B) / log(A). To find the unkonwn exponent, X, simply solve the division problem. The result will be the unknown exponent.

solving for exponents practice problems

To fully understand this concept, it is important to utilize your knowledge through problems. Rather than creating your own, you can simply use some of the ones from our collection of solving for exponents problems below. They are categorized into three different categories: easy, medium, and hard. It is recommended you begin with the easy problems and work your way up from there. If you are having difficulties solving any of the problems, you may use our solving for exponents calculator which will calculate the answer and provide steps on how the problem was solved. You may also use the calculator to check you got the correct answer.

easy:

1.) Solve for x when 3

^{x}= 210.

2.) Solve for x when 5

^{x}= 625.

3.) Solve for x when 8

^{x}= 233.

4.) Solve for x when 6

^{x}= 120.

5.) Solve for x when 9

^{x}= 100.

6.) Solve for x when 12

^{x}= 542.

7.) Solve for x when 2

^{x}= 299.

8.) Solve for x when 4

^{x}= 485.

9.) Solve for x when 6

^{x}= 892.

10.) Solve for x when 3

^{x}= 343.

medium:

1.) Solve for x when 12

^{x}= 1,210.

2.) Solve for x when 62

^{x}= 6,525.

3.) Solve for x when 55

^{x}= 2.33.

4.) Solve for x when 9

^{x}= 12,431.

5.) Solve for x when 13

^{x}= 5,413.

6.) Solve for x when 16

^{x}= 43.

7.) Solve for x when 12

^{x}= 4.1324.

8.) Solve for x when 37

^{x}= 5.65.

9.) Solve for x when 46

^{x}= 234.43.

10.) Solve for x when 42

^{x}= 6,342.

hard:

1.) Solve for x when 123

^{x}= 5,433.

2.) Solve for x when 531

^{x}= 54,143.

3.) Solve for x when 83

^{x}= 18.44.

4.) Solve for x when 655

^{x}= 541.

5.) Solve for x when 945

^{x}= 944.

6.) Solve for x when 102

^{x}= 43,143.

7.) Solve for x when 254

^{x}= 14,299.

8.) Solve for x when 412

^{x}= 44,123.

9.) Solve for x when 654

^{x}= 54,892.

10.) Solve for x when 3,750

^{x}= 108,343.