How to Solve an Exponential Equation

Step-by-step solution

1. Write the right side as a power of 3.

   $$81 = 3^4$$

   Why: Both sides need the same base to compare exponents.

2. Replace 81 in the equation.

   $$3^x = 3^4$$

   Why: The equation now has one base on each side.

3. Match the exponents.

   $$x = 4$$

   Why: Equal powers with the same base have equal exponents.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $2^x = 16$

   Show answer

   $x = 4$

2. 2

   $5^x = 125$

   Show answer

   $x = 3$

3. 3

   $10^x = 1000$

   Show answer

   $x = 3$

4. 4

   $4^x = 64$

   Show answer

   $x = 3$

5. 5

   $7^x = 1$

   Show answer

   $x = 0$