Question

1. rewrite the equation $16^{-1}=\frac{1}{16}$ in logarithmic form.

Explanation:

Step1: Recall the exponential - logarithmic conversion formula

The exponential form is \(a^{x}=y\), and its corresponding logarithmic form is \(\log_{a}y = x\), where \(a>0,a
eq1\).

Step2: Identify \(a\), \(x\) and \(y\) from the given equation

Given the equation \(16^{- 1}=\frac{1}{16}\), we can see that \(a = 16\), \(x=-1\), and \(y=\frac{1}{16}\).

Step3: Apply the conversion formula

Substitute \(a = 16\), \(x=-1\) and \(y = \frac{1}{16}\) into the logarithmic form formula \(\log_{a}y=x\). We get \(\log_{16}\frac{1}{16}=-1\).

Answer:

\(\log_{16}\frac{1}{16}=-1\)