take ln to y=x^10-3?

Question

if i take ln to both sides, does it turn into lny=lnx^10-ln3?

Answer 1

y=x^10-3
taking ln on both side
ln y = ln(x^10-3)
ln y = ln x^10 - ln 3
ln y = 10 ln x/3

I think it's like that

Answer 2

If we take the natural log of both sides we get:

y = x^10 - 3

ln(y) = ln(x^10 - 3)

So the answer is no. You can't break up the log of a sum like that.

Answer 3

Well, yes and no...

y = x^(10^–3)
ln(y) = ln(x^(10^–3))

So far so good, but because ln(a^b) = b ln(a) you should really write this as

ln(y) = (10^–3)ln(x)

Looks nicer, doesn't it?