Question: The equation in exponential form. \[ \log_{18} \frac{1}{324} = -2 \] Options: 1. \(18^{-2} =…

The equation in exponential form.

\[ \log_{18} \frac{1}{324} = -2 \]

Options:

1. \(18^{-2} = \frac{1}{324}\)
2. \(-2^{18} = \frac{1}{324}\)
3. \(-2 = 18^{\frac{1}{324}}\)
4. \(18^{-2} = -\frac{1}{324}\)

Solution

To convert the logarithmic equation to exponential form, we’ll use the property: If \(\log_b a = c\), then \(b^c = a\). Given: \[ \log_{18} \frac{1}{324} = -2 \] Using the property, we convert this to exponential form: \[ 18^{-2} = \frac{1}{324} \] Therefore, the correct choice is: \(18^{-2} = \frac{1}{324}\)