Problem
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. \[ \ln (12)+8 \ln (x)-9 \ln (y) \] Answer Tables Keyboard Shor If you wish to enter log or ln, you must use the keypad.
Solution
Step 1 ：Given the expression \(\ln (12)+8 \ln (x)-9 \ln (y)\)
Step 2 ：Using the properties of logarithms, we can rewrite the expression as \(\ln (12) + \ln (x^8) - \ln (y^9)\)
Step 3 ：Further simplifying, we get \(\ln (12x^8/y^9)\)
Step 4 ：Thus, the simplified form of the given expression is \(\boxed{\ln (12x^8/y^9)}\)
