Question

Express the following as a single logarithm:

`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`

Answer 1

`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`

= `"log"(3^4)/(2^3) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(5^2)/(3^2)`

= log3⁴ - log2³ - 2log3 + 2log5 + 3log2 - 3log5 + log5² - log3²
= 4log3 - 3log2 - 2log3 + 2log5 + 3log2 - 3log5 + 2log5 - 2log3
= log5.