To solve the equation \( 2x^{32} = 16 \), we can start by isolating \( x^{32} \).
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Divide both sides by 2: \[ x^{32} = \frac{16}{2} = 8 \]
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Next, we can express 8 as a power of 2: \[ 8 = 2^3 \]
So we have: \[ x^{32} = 2^3 \]
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Now, we can rewrite the equation: \[ x^{32} = 2^3 \]
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To solve for \( x \), we can take the 32nd root of both sides: \[ x = (2^3)^{\frac{1}{32}} = 2^{\frac{3}{32}} \]
We can evaluate this approximately or leave it as \( 2^{\frac{3}{32}} \).
If we approximate this value:
- \( 2^{\frac{3}{32}} \) is approximately equal to about 1.1 (not exactly one of the options).
None of the given options (84, 4, no solution, or 8) match \( 2^{\frac{3}{32}} \).
So, the best answer given these options is: no solution
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