Solve for x: 4^x = 64

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Multiple Choice

Solve for x: 4^x = 64

Explanation:
The main idea is that when you have the same positive base, the exponents must be equal if the powers are equal. Here, 64 can be written as a power of 4: 4^3 = 64, since 4^1 = 4, 4^2 = 16, and 4^3 = 64. So the equation 4^x = 64 becomes 4^x = 4^3. With the same base, the exponents are equal, giving x = 3. You can also see it by rewriting with base 2: 4^x = (2^2)^x = 2^(2x) and 64 = 2^6, so 2x = 6, hence x = 3. Either way, x equals 3.

The main idea is that when you have the same positive base, the exponents must be equal if the powers are equal. Here, 64 can be written as a power of 4: 4^3 = 64, since 4^1 = 4, 4^2 = 16, and 4^3 = 64. So the equation 4^x = 64 becomes 4^x = 4^3. With the same base, the exponents are equal, giving x = 3.

You can also see it by rewriting with base 2: 4^x = (2^2)^x = 2^(2x) and 64 = 2^6, so 2x = 6, hence x = 3. Either way, x equals 3.

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