Logarithms

[carebear]

Can you please help me with 2 things:

1. What is the name given to x in log₂x? Is it the argument?

2. I realize that in the above example x can never be negative or zero, BUT can the base of a logarithm be negative? For example, when I switch this to exponential form, it should work....is it okay to have a negative base?

log_(-2)16=4 (-2)⁴ = 16

Thank you very much for your help.

 

[pka]

1. What is the name given to x in log₂x? Is it the argument?
CORRECT

2. I realize that in the above example x can never be negative or zero, BUT can the base of a logarithm be negative?

The base of any logarithm is a positive number other than one.

 

[soroban]

Hello, carebear!

1. What is the name given to \(\displaystyle x\) in \(\displaystyle \log_2x\) ?
Is it the argument?

I believe that is the proper term.

2. I realize that in the above example \(\displaystyle x\) can never be negative or zero.
But can the base of a logarithm be negative?
For example, when I switch this to exponential form, it should work. . .
. . \(\displaystyle \log_{(-2)}16 \:=\:4 \quad\Rightarrow\quad (-2)^4 = 16\)

Is it okay to have a negative base? .No

The function does not exist for zillions of values of \(\displaystyle x.\)
Convert to exponential form and we can see why.

. . \(\displaystyle \log_{(-2)} 4 \:=\:y \quad\Rightarrow\quad (-2)^y \:=\:4\)