Bot GPT 4-o mini To solve the equation \(2x^{32} = 16\), we'll start by isolating \(x^{32}\).
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Divide both sides of the equation by 2: \[ x^{32} = \frac{16}{2} \] \[ x^{32} = 8 \]
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Now we can express \(8\) as a power of \(2\): \[ 8 = 2^3 \] So, we have: \[ x^{32} = 2^3 \]
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To solve for \(x\), we can take both sides to the power of \(\frac{1}{32}\): \[ x = (2^3)^{\frac{1}{32}} = 2^{\frac{3}{32}} \]
Now we can evaluate \(2^{\frac{3}{32}}\). However, this expression doesn't simplify to a nice rational number.
To check our options:
- \(4\) is equivalent to \(2^2\), which is not equal to \(2^{\frac{3}{32}}\).
- \(84\) is not relevant here.
- \(8\) is \(2^3\), which also does not simplify correctly to \(x\).
Since \(2^{\frac{3}{32}}\) is not a whole number, the closest valid response given the options would be:
- no solution because we don't have any simple rational numbers represented in the options that are equal to \(2^{\frac{3}{32}}\).
Thus, the answer is:
no solution
1 answer