Test Index

RRB NTPC Mains or Stage 2 Model Paper 4 with solutions

© examsnet.com

Question : 17 of 120

Marks: +1, -0

8^{9.4} \times 4^{12.8} \times 64^{8.1} = 16^{?}

41.8
16.2
18.4
25.6

Solution:

Concept:

Convert all bases to prime base

2

, then equate powers.

Explanation:

Let the missing exponent be

x

.

Write

8=2^3

,

4=2^2

,

64=2^6

, and

16=2^4

.

Left side

=2^{3\times 9.4}\times 2^{2\times 12.8}\times 2^{6\times 8.1}

.

Add the exponents:

28.2+25.6+48.6=102.4

.

So, left side

=2^{102.4}

.

Right side

=(2^4)^x=2^{4x}

.

Equate powers:

4x=102.4

.

Thus,

x=\frac{102.4}{4}=25.6

.

Answer:

x=25.6

, which matches option D.

© examsnet.com

Go to Question:

Prev Question

Next Question