SOLUTION: How would I solve: ln ( x + 3 ) - ln ( x + 2 ) = 5 I know that you have to divide so I got: ln ( x+3/x+2) = 5 but I couldn't get any farther than that.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How would I solve: ln ( x + 3 ) - ln ( x + 2 ) = 5 I know that you have to divide so I got: ln ( x+3/x+2) = 5 but I couldn't get any farther than that.      Log On


   



Question 258691: How would I solve:
ln ( x + 3 ) - ln ( x + 2 ) = 5
I know that you have to divide so I got: ln ( x+3/x+2) = 5 but I couldn't get any farther than that.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


You just need to learn how to change a logarithm equation 
to an exponential equation:

If it's a log base b equation like this:

log%28b%2C%28%22EXPRESSION%231%22%29%29+=+%22EXPRESSION%232%22

you change it to this exponential form:

%22EXPRESSION%231%22=b%5E%28%22EXPRESSION%232%22%29

If it's a natural log equation, (like yours), like this:

ln%28%22EXPRESSION%231%22%29+=+%22EXPRESSION%232%22

you change it to this exponential form:

%22EXPRESSION%231%22=e%5E%28%22EXPRESSION%232%22%29

You can think of the instructions
this way:


Drop the log on one side and put the 
other side as an exponent of the base.


So when you got here:

ln+%28+%28x%2B3%29%2F%28x%2B2%29%29+=+5

You drop the "ln" on the left and put the right side
as an exponent of "e" like this:

%28x%2B3%29%2F%28x%2B2%29+=+e%5E5

Then you clear of fractions by multiplying
both side by %28x%2B2%29

x%2B3=e%5E5%28x%2B2%29

Distribute on the right:

x%2B3=e%5E5%2Ax%2B2e%5E5%29

Get the x-terms on the left
and the other terms on the right:

x-e%5E5%2Ax=2e%5E5-3

Factor out x on the left:

x%281-e%5E5%29=2e%5E5-3

Divide both sides by 1-e%5E5

x=%282e%5E5-3%29%2F%281-e%5E5%29

You can either leave it like that or
get your calculator and punch it out
and get the decimal approximation:

x=-1.993216345

Edwin