Question

What is the value of log 7 343?–3 -1/3 1/3 3

Answer 1

Answer: 3

Explanation:

Given :

`Log_(7)` 343

We need to write 343 in index form of 7.

343 is the same as
`7^(3)` , replacing 343 with
`7^(3)` , we have

`Log_(7)`
`7^(3)`

Recall one on the law of Logarithm :

`Log_(a)`
`b^(c)` can be written as c
`Log_(a)`b

So,
`Log_(7)`
`7^(3)` can be written as ;

3
`Log_(7)` 7

Also from the laws of Logarithms ,
`Log_(a)` a = 1

so , Log_{7}[/tex] 7 = 1

The solution then becomes

3 x 1 = 3

Therefore :

`Log_(7)` 343 = 3