Problem 1 - College Algebra Essentials

Question

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$2^{x}=64$$

Step-by-Step Solution

Answer

The solution to the equation \(2^{x}=64\) is \(x=6\)

Step 1: Express Both Sides as Powers of the Same Base

Start by expressing 64 as a power of 2. We know that \(64=2^{6}\), so we can rewrite the equation as \(2^{x}=2^{6}\)

Step 2: Equating the Exponents

When the bases are equal, the exponents must also be equal for the equation to hold true. So we can set the exponents equal to each other to get \(x=6\)