Question

Express the following in terms of log 2 and log 3: `"log"(225)/(16) - 2"log"(5)/(9) + "log"(2/3)^5`

Answer 1

`"log"(225)/(16) - 2"log"(5)/(9) + "log"(2/3)^5`

= `"log"(225)/(16) - 2"log"(5)/(9) + 5"log"(2)/(3)`

= log225 - log16 - 2[log5 - log9] + 5[log2 - log3]
= log(5² x 3²) - log2⁴ - 2[log5 - log3²] + 5[log2 - log3]
= log5² + log3² - 4log2 - 2[log 5 - 2log3] + 5[log2 - log3]
= 2log5 + 2log3 - 4log2 - 2log5 + 4log3 + 5log2 - 5log3
= log2 + log3.