Not to barge in, but I didn't know log graphs had a horizontal asymptote?
I'm a little confused, can someone explain?
Cheers.
They don't, it was a poor choice of words on Special At Specialist's part, however he was correct in saying "that the curve will never end up horizontal, it will only approach zero gradient, so it will never head due east."
It is correct that if a function exhibits the behaviour of a horizontal asymptote e.g. as
for some
that this implies as
. However it is not true the other way around i.e. As
then
for some
.
Take
)
for example, where
.
Based on the above we can say that as
.
However, if the false implication was true then we would say
)
has a horizontal asymptote. Why have we never drawn one in during our years of logarithmic study then? Well
is strictly increasing for all
, so it can't have a horizontal asymptote.
Feel free to read
this post and its accompanying comments for some discussion/proofs/proper explanations on why the logarithm function doesn't have a horizontal asymptote.
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