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(1)/(16)=-4 \\ \text{This is equivalent to,} \\ 2^(-4)=(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)=(1)/(a^x)`

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

`\begin{gathered} 2^(-4)=(1)/(16) \\ (1)/(2^4)=(1)/(16)^{} \\ (1)/(16)=(1)/(16) \end{gathered}`

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

`\log _2(1)/(16)=2^(-4)`