Questions: Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. log(m^-2) log(m^-2)=

Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible.

log(m^-2)

log(m^-2)=

Transcript text: Use properties of logarithms to expand each logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. \[ \begin{array}{c} \log \left(m^{-2}\right) \\ \log \left(m^{-2}\right)= \end{array} \]

Solution

Solution Steps

Step 1: Original Expression

We start with the logarithmic expression: \[ \log \left(m^{-2}\right) \]

Step 2: Apply the Power Rule

Using the power rule of logarithms, which states that \(\log(a^b) = b \cdot \log(a)\), we can expand the expression: \[ \log \left(m^{-2}\right) = -2 \cdot \log(m) \]