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-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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