Rajasthan Police Constable Model Paper 6

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Question : 40 of 150

Marks: +1, -0

If

16^{2x+6}

= 64, then what is the value x1

-9/4
9/4
-18/4
18/4

Solution:

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)^{-m} = 1/a^m

5.

(a)^{m/n}= (√a^{m})^{1/n}

6. (a)^0 = 1
Given,
⇒

16^{2x+6}

= 64
⇒

(4^2) ^{2x+6}= (4)^3

⇒

( 4)^{4x + 12}

=

(4)^3

⇒ 4x + 12 = 3
⇒ 4x = -9
⇒ x = -9/4
∴ x

^{1 }

= -9/4

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