Question

How do you calculate `log_(343) 49`?

Answer 1

`log_343 49 = 2/3` (method below)

Explanation:

Notice that
`color(white)("XXX")49=7^2`
and
`color(white)("XXX")343=7^3`

and remember that `log_b a = k` is equivalent to `b^k=a`

Let `color(blue)(log_343 49=k)`

`color(white)("XXX")rArr 343^k=49`

`color(white)("XXX")rArr (7^3)^k=7^2`

`color(white)("XXX")rArr 7^(3k)=7^2`

`color(white)("XXX")rArr 3k=2`

`color(white)("XXX")rArr color(blue)(k=2/3)`