Problem 870

Solve the exponential equation by expressing each side as a power of the same base and then equating exponents.

2^x = 8192

 

Solution:-

 

To solve the exponential equation, start by expressing each side as the power of the same base. Since the base on the side is 2, use the guess and check method to determine the power of that equals the right side.

Now express both sides of the equation as the power of the same base.

2^x = 8192

2^x = 2¹³

x = 13

Therefore, the solution set is {13}.