Question

what's the restriction for log(x)

Answer 1

is it x >= 0 ?

Answer 2

no

Answer 3

and base >= 0?

Answer 4

\(x>0\)

Answer 5

what about base?

Answer 6

\[
b>1
\]

Answer 7

No it can be >0.

Answer 8

the base has to be positive, but it does not have to be greater than one, but rather greater than 0 and not equal to one

Answer 9

Yeah, sorry, \(b>0, b \ne 1\)

Answer 10

why not equal to 1 ?

Answer 11

i.e. \(b>0,b\neq 1\)
if the base is 1 you do not have an exponential function, but rather a constant, since \(1^x=1\)

Answer 12

and why can't base be 0?

Answer 13

i mean, 0^x is a function no?

Answer 14

because \(0^x=0\)

Answer 15

sure just like \(1^x=1\) but it is a constant, not an exponential function

Answer 16

Technically \(\log_bx\) can have \(x \epsilon\mathbb{R}/\{0\}\) since the result exists, it's just imaginary for negative x values.

Answer 17

also some people argue about what \(0^0\) is but no matter it is excluded as a base

Answer 18

So if i understood correctly, in both log and exponent functions, there are 2 restrictions, one for the base and one for the exponent?

Answer 19

@artofspeed again, it depends if you only care for reals, complex, or surreal numbers.

Answer 20

only real number plz..