Verified by Ajay Kumar
Given that \(343\times(\sqrt7)^n=49^4\), find n.
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Answer: B
Write all terms with base 7. \(343=7^3\), \(\sqrt7=7^{1/2}\), and \(49^4=(7^2)^4=7^8\). Thus, \(7^3\times7^{n/2}=7^8\). Therefore, \(3+\frac{n}{2}=8\), so \(\frac{n}{2}=5\) and \(n=10\). Trick: Convert all terms to the same base and compare exponents.
दिया गया है कि \(343\times(\sqrt7)^n=49^4\), n ज्ञात कीजिए।
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10
9
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उत्तर: B
सभी पदों को आधार 7 में लिखें। \(343=7^3\), \(\sqrt7=7^{1/2}\) और \(49^4=(7^2)^4=7^8\)। अतः \(7^3\times7^{n/2}=7^8\)। इसलिए \(3+\frac{n}{2}=8\), अर्थात \(\frac{n}{2}=5\) और \(n=10\)। ट्रिक: सभी पदों को एक ही आधार में बदलकर घातों की तुलना करें।
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