Delhi Police Constable Exam Model Paper 8

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Question : 79 of 100

Marks: +1, -0

If

(√3)^ 5 × 9^ 2 = 3^ n × 3√3

, find the value of n.

5
6
7
8

Solution:

By using the law of indices∶
Laws of Indices∶-
1-∶

a^m×a^n=a^{m + n}

2-∶

a^m÷a^n=a^{m-n}

3-∶ [(a^m)^n]=a^{mn}

4-∶ (a)^{(1/m)}= m_√a

5-∶ (a)^(-m)=1/a^m

6∶ (a)^(m/n)=n_√a^m

7-∶

(a)^0=1

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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