Question

Express the following as a single logarithm:

`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`

Answer 1

`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`

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

= 2log 2⁴ - 2 log 5² - 3{log 2³ - log 5} + log 2 + log 5 + log 3²
= 2 x 4 log 2 - 2 x 2 log 5 - 3 x 3 log 2 + 3 log 5 + log 2 log 5 + 2 log 3
= 8 log 2 - 4 log 5 - 9 log 2 + 3 log 5 + log 2 + log 5 + 2 log 3
= 2 log 3
= log 3²
= log 9.