logarithms

[unkempt palm]

i taught of changing bases inside out but that did not work

[gusty oracle]

what can you say of log_b(x) if x > b ?

[unkempt palm]

the answer > 1

[gusty oracle]

wait that won't be useful

sorry

when x is between b and b^2

what can you say about log_b(x) ?

[unkempt palm]

hmmmm

x^2 will be between b^2 and b^4?

@gusty oracle

[gusty oracle]

not quite

[unkempt palm]

what answer should I say?

[gusty oracle]

log_b is the reciprocal of x -> b^x

so x will be between 1 and 2

you compare the exponents

so what x^2 equals is not defined here

so your original answer is correct

we'll get some log(negative) at some point

[unkempt palm]

so x = 1?

we do not have to evaluate it we can just think about what values x have to be?

[gusty oracle]

what.

[unkempt palm]

oh wait nvm

[gusty oracle]

it's not an integer

[gusty oracle]

well log_6(7) is between 1 and 2

[unkempt palm]

yes

so it will get negative

in the next one

[gusty oracle]

yes

so the next one is not defined

[unkempt palm]

ooh

that makes sense

it looks complicated but now it seems a lot easier

so its not defined and there are no real values?

[gusty oracle]

yes

so 0 is correct

well it could be defined in the complex world but real values cannot give complex numbers when squared

[unkempt palm]

😎

sounds good

thanks

[gusty oracle]

np 😄

[unkempt palm]

I have one more than I am not sure how to do

I realize that they are in same base, base 10, but I looked back at my properties and I wasn't sure which one to do because they are seperate equations