Question 15 - of 18 Step 1 of 1 $00: 48: 10$ Use the properties of logarithms to condense the following expression as much as possible, writing the answer as a single term with a coefficient of 1. All exponents should be positive. \[ \ln (12)+9 \ln (x)-8 \ln (y) \] Answer 5 Points Keypad Keyboard Shortcuts If you wish to enter log or ln, you must use the keypad.

Step 1 ：Given the expression \(\ln (12)+9 \ln (x)-8 \ln (y)\)

Step 2 ：We can use the properties of logarithms to simplify this expression. The properties of logarithms state that \(\ln(a) + \ln(b) = \ln(ab)\) and \(\ln(a) - \ln(b) = \ln(\frac{a}{b})\). Also, \(\ln(a^n) = n \ln(a)\).

Step 3 ：Applying these properties, we can rewrite the expression as \(\ln(12) + \ln(x^9) - \ln(y^8)\)

Step 4 ：This can be further simplified to \(\ln(12 \cdot x^9) - \ln(y^8)\)

Step 5 ：Finally, we can simplify this to \(\ln(\frac{12 \cdot x^9}{y^8})\)

Step 6 ：Thus, the simplified form of the given expression is \(\boxed{\ln \left(\frac{12x^9}{y^8}\right)}\)