Question

Simplify the attached question

Answer 1

Given

$\begin{cases}Log_{0.125 }^8 \end{cases}$

To find

• simplify this log

Solution

Let this log give k in Rhs

Therefore

$\sf\:Log_{0.125 }^8=k$

$\implies\sf\:Log_{0.125 }^8=k$

$\implies\sf\frac{125}{1000}^k=8$

$\implies\sf\frac{5}{10}^{3k}=2^3$

$\implies\sf(\frac{1}{2})^{3k}=2^3$

$\implies\sf(\frac{1}{2})^{3k}=2^3$

$\implies\tt\:2^{-3k}=2^3$

=>k = -1