Question

find the logarithm of 0.125 to the base 2

Answer 1

$\log_{2}0.125=-3$

Step-by-step explanation:

Let $x=\log_{2}0.125$

Evaluate, $\log_{2}0.125=?$

∴$x=\log_{2}(\dfrac{125}{1000} )$

⇒ $x=\log_{2}(\dfrac{1}{8} )$

⇒ $x=\log_{2}((\dfrac{1}{2} ))^{3}$

⇒ $x=\log_{2}(2)^{-3}$

⇒ $x=-3\log_{2}(2)$

⇒$x=-3$

[ ∵ $\log_aa=1$]

Hence, $\log_{2}0.125=-3$.