Solving for Exponents

contents: solving for exponents calculator:
^ X =


X = 0
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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 3x = 210.
2.) Solve for x when 5x = 625.
3.) Solve for x when 8x = 233.
4.) Solve for x when 6x = 120.
5.) Solve for x when 9x = 100.
6.) Solve for x when 12x = 542.
7.) Solve for x when 2x = 299.
8.) Solve for x when 4x = 485.
9.) Solve for x when 6x = 892.
10.) Solve for x when 3x = 343.

        medium:

1.) Solve for x when 12x = 1,210.
2.) Solve for x when 62x = 6,525.
3.) Solve for x when 55x = 2.33.
4.) Solve for x when 9x = 12,431.
5.) Solve for x when 13x = 5,413.
6.) Solve for x when 16x = 43.
7.) Solve for x when 12x = 4.1324.
8.) Solve for x when 37x = 5.65.
9.) Solve for x when 46x = 234.43.
10.) Solve for x when 42x = 6,342.

        hard:

1.) Solve for x when 123x = 5,433.
2.) Solve for x when 531x = 54,143.
3.) Solve for x when 83x = 18.44.
4.) Solve for x when 655x = 541.
5.) Solve for x when 945x = 944.
6.) Solve for x when 102x = 43,143.
7.) Solve for x when 254x = 14,299.
8.) Solve for x when 412x = 44,123.
9.) Solve for x when 654x = 54,892.
10.) Solve for x when 3,750x = 108,343.