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21 Feb 2023, 14:02
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If \(x > 0\) and \(x^{(3*x^{12})}=4\), what is the value of \(x\) ?
A. \(\sqrt[12]{2}\)
B. \(\sqrt[6]{2}\)
C. \(\sqrt[3]{2}\)
D. \(\sqrt{3}\)
E. \(\sqrt{2}\)
A. \(\sqrt[12]{2}\)
B. \(\sqrt[6]{2}\)
C. \(\sqrt[3]{2}\)
D. \(\sqrt{3}\)
E. \(\sqrt{2}\)
21 Feb 2023, 14:02
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Official Solution:
If \(x > 0\) and \(x^{(3*x^{12})}=4\), what is the value of \(x\) ?
A. \(\sqrt[12]{2}\)
B. \(\sqrt[6]{2}\)
C. \(\sqrt[3]{2}\)
D. \(\sqrt{3}\)
E. \(\sqrt{2}\)
\(x^{(3*x^{12})}=4\);
Take to the fourth power:
\((x^{(3*x^{12})})^4=4^4\);
\(x^{(12*x^{12})}=4^4\);
\((x^{12})^{(x^{12})} =4^4\);
\(x^{12}=4=2^2\);
\(x=(2^2)^{(\frac{1}{12})}\);
\(x=2^{(\frac{1}{6})}\);
\(x=\sqrt[6]{2}\)
Answer: B
If \(x > 0\) and \(x^{(3*x^{12})}=4\), what is the value of \(x\) ?
A. \(\sqrt[12]{2}\)
B. \(\sqrt[6]{2}\)
C. \(\sqrt[3]{2}\)
D. \(\sqrt{3}\)
E. \(\sqrt{2}\)
\(x^{(3*x^{12})}=4\);
Take to the fourth power:
\((x^{(3*x^{12})})^4=4^4\);
\(x^{(12*x^{12})}=4^4\);
\((x^{12})^{(x^{12})} =4^4\);
\(x^{12}=4=2^2\);
\(x=(2^2)^{(\frac{1}{12})}\);
\(x=2^{(\frac{1}{6})}\);
\(x=\sqrt[6]{2}\)
Answer: B
24 May 2024, 17:41
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I think this is a high-quality question and I agree with explanation.
