Question

Calculate the value of `p` in `log49^2=plog7` ?

Answer 1

`p = 4`

Explanation:

`log 49^2=p log 7 rArr log(7^2)^2=log 7^p` or

`log 7^4= log 7^p rArr p = 4`

Answer 2

`p=4`

Explanation:

`Log49^2 = pLog7`

Solution

Recall `->` `aLogb = Logb^a`

`:.` `Log49^2 = Log7^p`

`Log7^(2(2)) = Log7^p`

`Log7^4 = Log7^p`

`cancel(Log7)^4 = cancel(Log7)^p`

Hence `4=p`

`p=4` `->` `Answer`

Answer 3

Use the following log law:

`logx^y=ylogx`

and the following index law:

`(x^a)^b=x^(ab)`

Simplify as follows:

`log49^2=plog7`

`rArrlog(7^2)^2=plog7`

`rArrlog7^4=plog7`

`rArr4log7=plog7`

`rArrp=4cancel(log7)/cancel(log7)`

`rArrp=4`