Question

Solve for the real value of x: 5/e^x+1=1

Answer 1

hmmm have you covered logarithms yet?

Answer 2

yes but it was so long ago i dont remember . i know it can be converted to natural log

Answer 3

Is it \[\frac{ 5 }{ e ^{x} +1}=1\]

Answer 4

yes !

Answer 5

Ok. First get x in the numerator by multiplying by the denominator on both sides.

Answer 6

That leaves us with.
\[5=e ^{x}+1\]

Answer 7

Following me so far?

Answer 8

did you cross multiply ?

Answer 9

That is one way to describe it. :)

Answer 10

okay i understand then , continue ?

Answer 11

Good. Now, continue working on isolating x by subtracting 1 on both sides.

Answer 12

Can you tell me what that leaves us with?

Answer 13

[5-1=e^{x}\]

Answer 14

Right or
\[4=e ^{x}\]

Answer 15

yeah sorry about the brackets
so do we have to convert to natural log ?

Answer 16

No worries. Yes, take the natural log of both sides.

Answer 17

What did you get?

Answer 18

does e = ln ?

Answer 19

No, but ln(e^x)=x
Natural log cancels out e^

Answer 20

is there a rule to use any time you're converting from e to ln or ln to e ?

Answer 21

I'm using the idea that ln(e)=1

Answer 22

im confused on how you convert then . how can you go from e^x to ln if when you times them they equal 1 ?

Answer 23

i understand you up to this point :(

Answer 24

Just a sec.

Answer 25

well one way to think about it is that lnx and e^x are inverse of each other
fo f(g(x))=x comes in handy here
whether you do this ln(e^x)=x or e^(lnx)=x you always end up with the identity function x

Answer 26

My bad. I gave you the wrong property. It should be
\[\log _{b}b ^{x}=x\]

Answer 27

So that brings us to ln4=x :)

Answer 28

lne=1 since e^1=e. you always thing of log and exponential as inverses
in other words they undo each other

Answer 29

you can also rewrite to make it more funcy
2ln2=x
do you know what property is this?

Answer 30

why are there two b's in joannas formula ? and no i dont

Answer 31

that logarithms base b
ln is logar base e

Answer 32

The base and what you are taking the log of are the same.

Answer 33

Natural log is log base e.

Answer 34

now think of this power that has base 2

Answer 35

we went from 2 to the power of 3=8
log helps us to undo this powering if u may say