Question 1056096
.
Write the logarithmic expression as a sum or difference of logarithms.

ln [(2x sqrt x^2+1)/(x+3)]
all of x^2+1 is inside the square root

So far I have ln(2) + ln(x) - ln(x+3)
I think ln(x+3) stays the same, but that square root stuff is really confusing. thank you to whoever helps me out!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
ln [(2x sqrt x^2+1)/(x+3)] = {{{ln(((2x)*sqrt(x^2+1))/(x+3))}}} = {{{ln(2x)}}} + {{{ln(sqrt(x^2+1))}}} - {{{ln(x+3)}}} = {{{ln(2)}}} + ln(x) + {{{(1/2)*ln(x^2+1)}}} - {{{ln(x+3)}}}.
</pre>


-------------------------
<U>Comment from student</U>: Thank you so much for helping me out. The explanation to the logarithm math question 
was answered by you extremely well. I understood everything (: 
-------------------------



<U>My response</U>: I am glad to hear it.


On logarithms, see a bunch of lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/what-is-the-logarithm.lesson>WHAT IS the logarithm</A>, 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/Properties-of-the-logarithm.lesson>Properties of the logarithm</A>, 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/change-of-base-formula-for-logarithms.lesson>Change of Base Formula for logarithms</A>, 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/How-to-solve-logarithmic-equations.lesson>Solving logarithmic equations</A>, 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/logarithm/Using-logarithms-to-solve-real-world-problems.lesson>Using logarithms to solve real world problems</A>, &nbsp;and

in this site.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Logarithms</U>".