CÂU 8 Rút gọn log_(2)5cdot ln2+4ln5

To simplify the expression \( \log_{2}5 \cdot \ln 2 + 4 \ln 5 \), we can use properties of logarithms. <br /><br />First, recall that \( \log_{a} b = \frac{\ln b}{\ln a} \). Therefore, we can rewrite \( \log_{2} 5 \) as \( \frac{\ln 5}{\ln 2} \).<br /><br />Substitute this into the expression:<br />\[ \log_{2}5 \cdot \ln 2 + 4 \ln 5 = \left( \frac{\ln 5}{\ln 2} \right) \cdot \ln 2 + 4 \ln 5 \]<br /><br />Next, simplify the term inside the parentheses:<br />\[ \left( \frac{\ln 5}{\ln 2} \right) \cdot \ln 2 = \ln 5 \]<br /><br />So the expression becomes:<br />\[ \ln 5 + 4 \ln 5 \]<br /><br />Combine like terms:<br />\[ \ln 5 + 4 \ln 5 = 5 \ln 5 \]<br /><br />Thus, the simplified form of the given expression is:<br />\[ 5 \ln 5 \]