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

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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.

It may want you to simplify e^5

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