Bot GPT 4-o mini To solve the equation \( 5x^{43} = 80 \), we want to isolate \( x \).
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First, divide both sides by 5: \[ x^{43} = \frac{80}{5} = 16 \]
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Now we have \( x^{43} = 16 \). To solve for \( x \), we take the 43rd root of both sides: \[ x = 16^{\frac{1}{43}} \]
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We need to determine \( 16^{\frac{1}{43}} \). Since \( 16 = 2^4 \), we can rewrite it: \[ x = (2^4)^{\frac{1}{43}} = 2^{\frac{4}{43}} \]
Now, let's compare \( x = 2^{\frac{4}{43}} \) to the given choices. The answer \( 2^{\frac{4}{43}} \) is approximately \( 1.061\) when calculated, which does not match any of the provided options (8, 16, 40.32, 12).
Since none of the choices correctly reflect \( 2^{\frac{4}{43}} \), the answer can't be correctly selected from the options provided.
The correct approach concludes \( x = 2^{\frac{4}{43}} \).
1 answer