Solve for x: 4^x = 64.

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Study for the 8th Grade FAST Mathematics Pre-Algebra Test. Enhance your skills with interactive flashcards and multiple choice questions, each containing hints and explanations to boost your comprehension and readiness for the exam. Get ready to ace your test!

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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