Question

The value of $\log _{200} 4$ lies between___

• A. $\frac{1}{3}$ and $\frac{1}{2}$
• B. $\frac{1}{4}$ and $\frac{1}{3}$
• C. 2 and 3
• D. 3 and 4

Answer 1

Answer: (B)

$\log _{200} 4$
Now, $4^2=16,4^3=64,4^4=256$
And, $64< 200< 256$
$\Rightarrow 4^3< 2000<4^4$
$\therefore$ The value of $\log _{200} 4$ lies between $\frac{1}{4}$ and $\frac{1}{3}$.