Log6 30-log6 2+log6 4

To simplify the expression \( \log_6 30 - \log_6 2 + \log_6 4 \), we can use the properties of logarithms.

1. Subtraction of Logarithms: The property \( \log_b a - \log_b c = \log_b \left( \frac{a}{c} \right) \) allows us to combine the first two terms: \[ \log_6 30 - \log_6 2 = \log_6 \left( \frac{30}{2} \right) = \log_6 15. \]

2. Addition of Logarithms: Next, we can use the property \( \log_b a + \log_b c = \log_b (a \cdot c) \) to combine the result with \( \log_6 4 \): \[ \log_6 15 + \log_6 4 = \log_6 (15 \cdot 4) = \log_6 60. \]

Thus, the simplified expression is: \[ \log_6 60. \]