Question

The exponential form of $0.125$ is $8^{-k}$

Then value of $5k$ is

Answer 1

We can write $\frac{125}{1000}={\left(\frac{5}{10}\right)}^3$
${\log }_{8}0.125=-1$
Now, we know that ${\log }_{b}a=\frac{\log a}{\log b}$
$\frac{\log 0.125}{\log 8}=-1$
$\log 0.125=\log 8^{-1}$
$0.125=8^{-1}$

k=1

Ans=5k=5