College Math Placement Practice Test

What is the value of x if 4^x = 64?

1. x = 1

2. x = 2

3. x = 3

4. x = 4

The correct answer is: x = 3

To find the value of \( x \) in the equation \( 4^x = 64 \), it can be helpful to express both sides of the equation as powers of the same base. First, notice that \( 4 \) can be rewritten as \( 2^2 \). Therefore, we can express \( 4^x \) as: \[ (2^2)^x = 2^{2x} \] Next, we need to rewrite \( 64 \) as a power of \( 2 \). We know that: \[ 64 = 2^6 \] Now, the equation \( 4^x = 64 \) becomes: \[ 2^{2x} = 2^6 \] Since the bases are the same, we can set the exponents equal to each other: \[ 2x = 6 \] To solve for \( x \), divide both sides by \( 2 \): \[ x = \frac{6}{2} = 3 \] Thus, the solution is \( x = 3 \). This confirms the correct answer as \( C \).