To rewrite \( \log(1/100) \) using the Power Rule of Logarithms, we can start by expressing \( 1/100 \) as \( 100^{-1} \). This way, we can apply the logarithmic properties.
-
Rewrite \( \log(1/100) \): \[ \log(1/100) = \log(100^{-1}) \]
-
Apply the Power Rule of Logarithms: \[ \log(100^{-1}) = -1 \cdot \log(100) \]
-
We know that \( 100 = 10^2 \), so we can further simplify \( \log(100) \): \[ \log(100) = \log(10^2) = 2 \log(10) \]
-
Substituting this back into our expression: \[ -1 \cdot \log(100) = -1 \cdot 2 \log(10) = -2 \log(10) \]
Thus, we can write the expression \( \log(1/100) \) as: \[ \log(1/100) = -2 \log(10) \]
If the logarithm is base 10, this can be approximated as: \[ \log(1/100) = -2 \]
So, the final rewritten form is: \[ \log(1/100) = -2 \log(10) \] or simply \( -2 \), if the base is 10.