That’s what confuses me, Alex. My friend sent this question to me and I think it’s quite odd. I also suspect there must be something missing or misquoted here. Anyway, I’m just an intermediate learner so I’m not sure what I think is correct.

A logarithm is what know in algebra as an exponent (without the second “is”)
I think it is the reduced form of this:
A logarithm is what that/which is known in algebra as an exponent.

Oh God!
How silly I was not to realise that typo (+_+)
I’m terribly sorry, Amy, I certainly meant “what known as”:

A logarithm is what known in algebra as an exponent
(I think it is the reduced form of “A logarithm is what that/which is known in algebra as an exponent”)

Many thanks and terribly sorry once again.
Nessie.

Once and for all: confronting school kids with the three terms ‘power’ ‘exponent’ and ‘logarithm’ without pointing out that they all essentially mean the same thing amounts to child abuse!

So is the duplicity of the usage of ‘power’:
Consider 2^3 = 8 ( ^ - ‘to the power of’):
You are told that “eight is the two to the power of three” i.e. ‘three’ being the power. Than you are told that “eight is a power of two” i.e. the ‘eight’ being the ‘power’

This kind of disregard is one of the causes of Maths being wrongly conceived as ‘more difficult’ than other subjects.

The book “Demathtifying - Demystifying Mathematics” shows systematically how these unnecessary obstacles can be easily circumvented.