Question

T or F?. log[1]512 is an expression that CANNOT be evaluated?

Answer 1

Building on what you've been taught already, if this expression could be evaluated, then there would be a number n such that

1^n = 512

Is there such a number, n?

Answer 2

would this also apply for n like the last question?

Answer 3

It's a different question, so evaluate this one on its face.

Let's experiment for a moment:

1^2 = 1
1^200 = 1
1^100000000000000000000 = 1

so making n big doesn't work

1^(-1) = 1
1^(-100000000000000) = 1

nor does making it large and negative

or small ... hmm ...

1^(1/2) = 1
1^(1/100000000000) = 1
and
1^(-1/10000000000) = 1

Answer 4

So do we think there is an n such that
\[1^n = 512\]
?

Answer 5

If there were such a number n, then log[1](512) = n.

Answer 6

But .......