Question

The value of ${\log }_{80}8$ lies between. ____

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

Answer 1

Answer: (A)

${\log }_{160}8$
Now, $8^2=64,8^3=512$
And, $64<160<512$
$\Rightarrow 8^2<160<8^3$
$\therefore$ The value of ${\log }_{160}8$ lies between $\frac{1}{3}$ and $\frac{1}{2}$.