Question

help please thank you

Answer 1

One of the rules of logarithms is as follows;

$\begin{gathered} \log _ab=x \\ Is\text{ equivalent to,} \\ a^x=b \end{gathered}$

We can now insert the corresponding values in the question provided, as shown below;

$\begin{gathered} \log _2\frac{1}{16}=-4 \\ \text{This is equivalent to,} \\ 2^{-4}=\frac{1}{16} \end{gathered}$

Note that, one of the rules of exponents, states that a number when raised to the power of a negative value, is equivalent to the reciprocal of that expression. An example is shown below;

$a^{-x}=\frac{1}{a^x}$

Therefore, our equation can now be re-written as follows;

$\begin{gathered} 2^{-4}=\frac{1}{16} \\ \frac{1}{2^4}=\frac{1}{16}^{} \\ \frac{1}{16}=\frac{1}{16} \end{gathered}$

However, the question requires the answer to be expressed in exponential form. Therefore,

$\log _2\frac{1}{16}=2^{-4}$