Question

Express the following as a single logarithm:

`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`

Answer 1

`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`

= 2log9 - 2log5 - 3log3 + 3log5 + log16 - log20
= 2log(3²) - 2log5 - 3log3 + 3log5 + log(4²) - log(5 x 4)
= 4log3 - 2log5 - 3log3 + 3log5 + 2log4 - log5 - log4
= (4 - 3)log3 + (-2-1+3)log5 + log4
= log3 + log4
= log(3 x 4)
= log12.