Question

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)

Answer 1

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)