Solve for x: 4^x = 64.

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Prepare for the 8th Grade FAST Mathematics Test with our Pre-Algebra quiz. Study with multiple choice questions, each with hints and explanations. Build your confidence and ensure you're ready to excel!

Multiple Choice

Solve for x: 4^x = 64.

Explanation:
This is about using exponent rules to solve for an unknown exponent by rewriting both sides with the same base. 64 can be written as 4^3, since 4 × 4 × 4 equals 64. So the equation becomes 4^x = 4^3. When the bases are the same, the exponents must be equal, which gives x = 3. Another way to see it is with base 2. Since 4 is 2^2, we have (2^2)^x = 2^(2x). And 64 is 2^6, so 2^(2x) = 2^6, leading to 2x = 6 and x = 3. Therefore, the solution is x = 3.

This is about using exponent rules to solve for an unknown exponent by rewriting both sides with the same base.

64 can be written as 4^3, since 4 × 4 × 4 equals 64. So the equation becomes 4^x = 4^3. When the bases are the same, the exponents must be equal, which gives x = 3.

Another way to see it is with base 2. Since 4 is 2^2, we have (2^2)^x = 2^(2x). And 64 is 2^6, so 2^(2x) = 2^6, leading to 2x = 6 and x = 3.

Therefore, the solution is x = 3.

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