Solving Exponential Equations Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Solve 3x=813^x = 81.

Solution

  1. 1
    Recognize that 8181 is a power of 33: 81=3481 = 3^4.
  2. 2
    So the equation becomes 3x=343^x = 3^4.
  3. 3
    Since the bases are equal, the exponents must be equal: x=4x = 4.

Answer

x=4x = 4
When both sides of an exponential equation can be written with the same base, set the exponents equal. This is the simplest method and avoids logarithms entirely. Always check if the number is a recognizable power of the base.

About Solving Exponential Equations

Solving exponential equations means finding the unknown variable trapped in an exponent by applying logarithms to both sides, using the power rule to bring the exponent down, and then isolating the variable with standard algebra.

Learn more about Solving Exponential Equations →

More Solving Exponential Equations Examples

Example 2 medium

Solve [formula].

Example 3 medium

Solve [formula].

Example 4 hard

Solve [formula].

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