Question

Express in terms of log 2 and log 3 :
`"log"75/16 - 2"log"5/9 + "log"32/243`

Answer 1

`"log"75/16 - 2"log"5/9 + "log"32/243`

= `"log"75/16 - "log"(5/9)^2 + "log"32/243`

= `"log"75/16 - "log"( 5/9 xx 5/9 ) + "log"32/243`

= `"log"75/16 - "log"25/81 + "log"32/243`

= `"log"((75/16)/(25/81))       .....[ log_am - log_an = log_a(m/n)]`

= `"log"(75/16) xx (81/25) + log(32/243)`

= `"log"( 3 xx 25)/16 xx 81/25 + "log"32/243`

= `"log"243/16 + "log"32/243`

= `"log"( 243/16 xx 32/243 )`     .....[log_am + log_an = log_amn]

= `"log"32/16`
= log 2