Use properties of logarithms to condense the following expression as much as possible , writing the answer as a single term with coefficient of 1. all exponents should be positive. ln(6)+9ln(x)-5ln(y)

1st transform the multiplication into power:

9ln(x) = ln(x)⁹

5ln(y)  = ln(x)⁵

ln(6) + ln(x)⁹ - ln(x)⁵
Now addition into multiplication:

ln(6) + ln(x)⁹   - ln(x)⁵    =  ln[(6).(x)⁹  -  ln(x)⁵
Now subtraction into division:

ln[(6).(x)⁹  -  ln(x)⁵ =ln[6x⁹/x⁵) ==> After simplification =ln(6x⁴)

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