Question

The value of ${\text{Log}}_{0.5}\text{16}$ is equal to :

Answer 1

Let ${\text{Log}}_{0.5}\text{16=x}$ then by using the definition of $\text{log}$ we can write it as

$16={(0.5)}^{\text{x}}$

Here $16$ can be written as $2^4$ and $0.5$ can be written as $\frac{5}{10}=\frac{1}{2}$

$$\begin{gathered} {\text{2}}^4\text{=(}\frac{1}{2}{\text{)}}^{\text{x}} \\ {\text{2}}^4{\text{=2}}^{-\text{x}} \end{gathered}$$

$\text{4=-x}$ ,$\text{x=-4}$

Here we use the law of exponent that ${\text{x}}^m{\text{=x}}^n$ then $\text{m=n}$

Hence the value of $\text{x}$ is $\text{-4}$.