Question

How do you apply ln and e?

Answer 1

Example?

Answer 2

ln(2) = 0.693
e^0.693 = 2

Answer 3

My example is e^x+5/e^5=3 and I have to work it out but didn't know what e equalled. Thank you!!!

Answer 4

Well, 5/e^5 = 0.0337
so you want x = ln(3 - 0.0337)

Answer 5

actually....there's a simpler way..

Answer 6

\[\huge \frac{e^{x+5}}{e^5} \implies e^{x + 5 - 5}\]
do you agree? @calchelp101 ? this is algebra..

Answer 7

Thank you! So would it now be e^x because it would cancel?

Answer 8

sorry of course
e^x+5/e^5= e^x

Answer 9

yup

Answer 10

so \[\huge e^x = 3\]
now use ln

Answer 11

You both are the best! Thank you so much! If you don't mind, can I ask one more question: I now have e^x=3 Should it be left like that or multiply 3 by 1/x?

Answer 12

Oh, okay! Thanks!

Answer 13

haha =)) guess that was answered quick

Answer 14

does ln cancel e?

Answer 15

yup

Answer 16

...well it depends on what you mean

Answer 17

can you show me what you're attempting to do?

Answer 18

Sure. I have e^x=3 so would I have x=3(ln) after applying?

Answer 19

So x=1.0986?

Answer 20

x = ln (3) haha

Answer 21

did they tell you to give exact value?

Answer 22

They didn't specify so I was going to give both.

Answer 23

oh i see...that value is right

Answer 24

Thank you so much! You are a lifesaver!

Answer 25

haha welcome ^_^

Answer 26

Only if you have time, I have another ln problem that has been giving me trouble!

Answer 27

sure

Answer 28

what's the problem?

Answer 29

ln(2x^6+3 square roots of x+8/(x-1)^4)

Answer 30

\[\huge \ln \left(\frac{2x^6 + 3\sqrt{x+8}}{(x-1)^4} \right)\]
is this the problem?

Answer 31

Yes

Answer 32

and you're supposed to.....expand it?

Answer 33

Yes and simplify

Answer 34

if i were you i'll start with quotient law first

Answer 35

So after I expand (x-1)^4 what should I do with the 3square roots of x+8?

Answer 36

nothing :D

Answer 37

there is no expansion for \[\ln (a+b)\]

Answer 38

Oh. Okay. On the bottom I have x^4-4x^3+8x^2-8x+4

Answer 39

well...not exactly...

Answer 40

this is not what i meant by expand...

Answer 41

You meant expand the ln?

Answer 42

lol that's the objective isnt it?

Answer 43

Well yes. haha

Answer 44

so expand the ln

Answer 45

use quotient law first

Answer 46

Okay, great! Thank you so much for your help!

Answer 47

welcome ^_^