##### ​ln x + ln(x-10) = 5 solve for x.

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ln x + ln(x-10) = 5 solve for x.

Sep 3rd, 2015

Thank you for the opportunity to help you with your question!

When adding 'ln' together, you can follow a general rule:

ln(a) + ln(b) = ln(a*b)     You just multiply whatever is in the parentheses to condense into one 'ln'.

Now for the problem:

ln(x) + ln(x-10) = 5

ln(x*(x-10)) = 5               Simplify the inner part of 'ln'

ln(x^2-10x) = 5               Now you take the 'e' to both sides to remove the 'ln' on the left-hand side to solve for 'x'.

e^(ln(x^2-10x)) = e^5      e^(lnx) = x     (This is another general rule)

x^2-10x = e^5                 You can remove an 'x' from both terms on left hand side, and set both equal to e^5.

x*(x-10) = e^5

x=e^5

x-10 = e^5

x = e^5+10

I'm not sure if that's what you're textbook is looking for or not.  It may have the answer condensed more.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 3rd, 2015

It may want you to simplify e^5

Sep 4th, 2015

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Sep 3rd, 2015
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Sep 3rd, 2015
Oct 22nd, 2017
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