If (\sqrt3)^5 \times 9^2 = 3^n \times 3\sqrt3 , find the value of n.

RRB Group-D Model Paper 15 with answers for online practice

Question : 5 of 100

Marks: +1, -0

(√3)^5 × 9^2 = 3^n × 3√3

, find the value of n.

Solution:

Given:

(√3)^5 × 9^2 = 3^n × 3√3

Concept Used:
By using the law of indices∶

a^m × a^n = a^{(m + n)}

a^m ÷ a^n = a^{(m – n)}

[(a^m)^n] = a^{mn}

(a)^(-m) = 1/a^m

(a)^(m/n) = n√a^m

(a)0 = 1
Calculation:
The equation will be solved as:

(√3)^5 × 9^2 = 3^n × 3√3

(√3)^4 × √3 × 9^2 = 3^n × 3√3

⇒

9√3 × 9^2 = 3^n × 3√3

⇒

3√3 × 3^5 = 3^n × 3√3

⇒

3^5 = 3^n

⇒ n = 5
∴ Value of n is 5

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