Question 116560
I am not even sure how to plug this in to my calculator.
I do not know what order to take to break this down. 
Please help me solve for x. 
<pre><font face = "book antiqua" size = 5 color = "indigo"><b>
a. {{{e^ln(3-2x)=5x}}} b. {{{ln(x) - ln(2) = 1}}}

First of all what you thought was "In" was really "ln" which
means "natural logarithm" or log<sub>e</sub> where e = 2.718...

Secondly, you don't plug anything into a calculator.  The 
calculator is a nice tool for saving time, but it doesn't save 
you from having to learn the rules of logarithms, and they
are all that are required here:

For (a) and (b) you need to learn the rule of logarithms:

{{{e^ln(A)=A}}}

For (b) you need to learn the rule of logarithms:

{{{ln(A) - ln(B) = ln(A/B)}}}

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

Using the first rule above on the left side, we have

{{{3-2x=5x}}}

which you can easily solve and get

{{{x=3/7}}}

(b)
{{{ln(x) - ln(2) = 1}}}

Using the second rule above on the left side, we have

{{{ln(x/2) = 1}}}

Now we raise e to the both sides power:

{{{e^ln(x/2) = e^1}}}

Using the first rule on the left side, and
erasing the 1 exponent on the right, we have:

{{{x/2 = e}}}

or

{{{x = 2e}}}

Edwin</pre>