Natural Logs n stuff

[biennerienno]

Hey all

Im working on a math problem:

e^(-z/d) = 1/10

my steps are:

1. Add ln to both sides

ln(e^(-z/d) = (ln 1) - (ln 10)

From here, I understand that on the right i get (-ln 10)
and i have been told that on the left of the = i can reduce to (-z/d)
Then i can reduce to:

(z/d) = ln 10

I think i may just be having a brain fart, but i cannot see how to bring down (-z/d)
and be able to put it in front of ln(e) (which i know = 1)

Anyway, im sure this is some simply algebra i forgot, so sorry if this is dumb!

 

[f95toli]

I am not sure what you are asking, but
ln(e^x)=x by definition
, logarithms are definied so that they have this propertie.

 

[f95toli]

And, by the way

ln(e)=1 because ln(e^1)=1

 

[Cogman]

that, and Log b (b) = 1. BTW you are not adding ln to both sides, but you are taking the ln of both sides, BIG diffrence. That is also the reasion you get -z/d = -ln(10) or z/d = ln(10). on another note.

log b (a^c) = c*log b (a). One of the definitions of logs.

 

[SirPsycho]

Log, Log... it's big, it's heavy, it's wood!

Sorry, I couldn't help it.