Questions: Use properties of logarithms to find the exact value of the expression. Do not use a calculator. log6 48 - log6 8 log6 48 - log6 8 = (Type an integer or a simplified fraction.)

Solution Steps

To solve the expression \(\log_{6} 48 - \log_{6} 8\), we can use the properties of logarithms. Specifically, we can use the property that \(\log_b (a) - \log_b (c) = \log_b \left(\frac{a}{c}\right)\). This allows us to combine the logarithms into a single logarithm.

We start with the expression: \[ \log_{6} 48 - \log_{6} 8 \] Using the property of logarithms \(\log_b (a) - \log_b (c) = \log_b \left(\frac{a}{c}\right)\), we can combine the logarithms: \[ \log_{6} 48 - \log_{6} 8 = \log_{6} \left(\frac{48}{8}\right) \]

Next, we simplify the fraction inside the logarithm: \[ \frac{48}{8} = 6 \] So the expression becomes: \[ \log_{6} 6 \]

We know that \(\log_b b = 1\) for any base \(b\). Therefore: \[ \log_{6} 6 = 1 \]

Final Answer