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Siddhartha Yadav

· started a discussion

· 1 Months ago

question error

Question:
\(\big( \sqrt[]{3}\big)^5× 9^2 = 3^n ×\sqrt[3]{3}\) , then the value of n is:
Options:
A) 8
B) 9
C) 4
D) 5
Solution:
Ans: (d)
\(\big( \sqrt[]{3}\big)^5× 9^2 = 3^n ×\sqrt[3]{3}\Leftrightarrow3^\left ( \frac {1}{2} \times5) \right )\times3^{(2\times2)}=3^{\left (n+1 \frac {1}{2} \right )}\)
\(\Leftrightarrow3^{\left ( \frac {5}{2} +4\right )}=3^{\left (n+ \frac {3}{2} \right )}⟺ n +\cfrac{3}{2}=\cfrac{13}{2}⟺ n = \left ( \cfrac {13}{2}-\cfrac{3}{2} \right )=\cfrac{10}{2}= 5.\)

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