Use the properties of logarithms to rewrite the logarithm if possible/Assume that all variables represent positive real numbers. 15) log_(4)(sqrt (5))/(3) 15) __ 16) log_(16)(19sqrt (r))/(s) 16) __ 17) log_(6)(7x+2y) 17) __

## Step 1<br />We are given three different logarithmic expressions and we need to rewrite them using the properties of logarithms. The properties of logarithms that we will use are:<br /><br />### **The quotient rule**: \( \log_b \frac{M}{N} = \log_b M - \log_b N \)<br />### **The power rule**: \( \log_b M^p = p \cdot \log_b M \)<br /><br />## Step 2<br />For the first expression, \( \log_{4}\frac {\sqrt {5}}{3} \), we can apply the quotient rule to separate the numerator and the denominator.<br /><br />## Step 3<br />For the second expression, \( \log_{16}\frac {19\sqrt {r}}{s} \), we can apply the quotient rule to separate the numerator and the denominator.<br /><br />## Step 4<br />For the third expression, \( \log_{6}(7x+2y) \), we can apply the power rule to separate the terms in the parentheses.