Test Index

UPSC NDA Math Model Paper 2

© examsnet.com

Question : 114 of 120

Marks: +1, -0

Solve:

\log_{2}(x+1)-\log_{2}(2-x)=3

2 / 3
3 / 7
1 / 2
5 / 3

Solution:

Given:

\log_{2}(x+1)-\log_{2}(2-x)=3

As we know that,

\log_{a}\left(\frac{x}{y}\right)=\log_{a} x-\log_{a} y

\Rightarrow\log_{2}(x+1)-\log_{2}(2-x)

=\log_{2}\left(\frac{x+1}{2-x}\right)=3

By applying antilog on both the sides we get,

\Rightarrow\frac{x+1}{2-x}=2^{3}=8

\Rightarrow x+1=8(2-x)

\Rightarrow 9x=15

⇒ x = 5 / 3

As,

\log_{2}(x+1)-\log_{2}(2-x)

is well defined.

Hence, x = 5 / 3

© examsnet.com

Go to Question:

Prev Question

Next Question