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 $\frac{1}{3}$.