Question 258691
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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(b,("EXPRESSION#1")) = "EXPRESSION#2"}}}

you change it to this exponential form:

{{{"EXPRESSION#1"=b^("EXPRESSION#2")}}}

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

{{{ln("EXPRESSION#1") = "EXPRESSION#2"}}}

you change it to this exponential form:

{{{"EXPRESSION#1"=e^("EXPRESSION#2")}}}

You can think of the instructions
this way:
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Drop the log on one side and put the 
other side as an exponent of the base.

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So when you got here:

{{{ln ( (x+3)/(x+2)) = 5}}}

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

{{{(x+3)/(x+2) = e^5}}}

Then you clear of fractions by multiplying
both side by {{{(x+2)}}}

{{{x+3=e^5(x+2)}}}

Distribute on the right:

{{{x+3=e^5*x+2e^5)}}}

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

{{{x-e^5*x=2e^5-3}}}

Factor out x on the left:

{{{x(1-e^5)=2e^5-3}}}

Divide both sides by {{{1-e^5}}}

{{{x=(2e^5-3)/(1-e^5)}}}

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

{{{x=-1.993216345}}}

Edwin</pre>