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If $$\root 3 \of {{3^n}} {\text{ = 27,}}$$ then the value of n is = ?
Answer & Solution
Correct Answer:
Option
A
According to question,
$$\eqalign{ & \root 3 \of {{3^n}} {\text{ = 27}} \cr & \Rightarrow {\left( {{3^n}} \right)^{\frac{1}{3}}} = {\left( 3 \right)^3} \cr & \Rightarrow {3^{\frac{n}{3}}} = {3^3} \cr & \Rightarrow \frac{n}{3} = 3 \cr & \Rightarrow n = 9 \cr} $$
$$\eqalign{ & \root 3 \of {{3^n}} {\text{ = 27}} \cr & \Rightarrow {\left( {{3^n}} \right)^{\frac{1}{3}}} = {\left( 3 \right)^3} \cr & \Rightarrow {3^{\frac{n}{3}}} = {3^3} \cr & \Rightarrow \frac{n}{3} = 3 \cr & \Rightarrow n = 9 \cr} $$
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