Question

Type the correct answer in the box log's​

Answer 1

log(7) will be the correct answer.

Explanation:

`\text{(14)/(3)}+\text{log}((11)/(5))-\text{log}((22)/(15))`By using law of logarithm to solve the given expression,

1).
`\text{log}(m)+\text{log}(n)=\text{log(mn)}`

2).
`\text{log(m)}-\text{log(n)}=\text{log}((m)/(n))`

By applying these rules, we can simplify the given expression,

`\text{log}((14)/(3))+\text{log}((11)/(5))-\text{log}((22)/(15))`

`\text{log}((14)/(3))+\text{log}((11)/(5))-\text{log}((22)/(15))=\text{log}(((14)/(3)* (11)/(5))/((22)/(15)))`

`=\text{log}(((154)/(15))/((22)/(15)))`

=
`\text{log}((154)/(15)* (15)/(22))`

= log(7)

Therefore, log(7) will be the correct answer.