Natural logarithm help?

Question

I have never dealt with logarithms before and they just popped up in my Chemistry class. Here's the problem:

ln (2/x) = 1.1

My book says to take the inverse of both sides, which gives you this:

2/x = 3

Can anyone explain this to me? I need to understand it so I can solve future problems. Thanks!

What does ^ mean?

What is e? Please break it down for me. I'm starting from scratch here.

Answer 1

The log of a number to a given base is the power to which the base must be raise in order to give the number.
Example 1
Log base 10 of 1000 = 3
10³ = 1000

Example 2
log base 2 of 16 = 4
2^4 = 16

In the given question, the base is base e which is a special number having value 2.718
ln (2/x) = 1.1
2 / x = 2.718^(1.1)
2 / x = 3

Answer 2

e is a very important constant in Mathematics.

it can be defined as the limit of (1+1/n)^n as n approaches infinity:

1+ 1+ 1/(1*2) + 1/(1*2*3) + 1/(1*2*3*4) + .......

you can get its numerical value from the internet.

It is the base to which natural logarithms are calculated.

Answer 3

log x y=a means x^a=y(^means to yhe power)
so taking natural log we get e^1.1=2/x so 2/x=3
as for the second question e is a transcendental number(irrational) which is the summation of the infinite series 1+1/1!+1/2!+1/3!........upto infinity. it is actually the binomial expansion of (1+x)^1/x where x=>0

Answer 4

ln is log base e. Ln and e are inverse functions so in order to undo a ln(x) you take e^(ln(x)) and get x. To solve your problem: e^(ln(2/x))=e^1.1 which gives 2/x=e^1.1 solving for x gives x=.665742167396. e^1.1=3.0041602395 . Your book approximates this to be 3 due to using significant digits. Hope this helps

Answer 5

ln(2/x) =1.1 by definition means that e to the power of 1.1 is 2/x. i dont have a calculator that has e right know but im almost sure eto the power of 1.1 must be close enough if not equal to 3

Answer 6

ln (2/x) = 1.1

e^1.1 = 2/x
x = 2/(e^1.1)

In a natural log, ln(answer) = exponent

Then take e^exponent = answer

Answer 7

e=2.714854