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# Ln question

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Hi,

How would I solve x+ln(x+6) = 7?

Would I have to bring the x to the other side and then solve using e^x-7=x+6 ?

Apr 28, 2020

#1
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$$x+ln(x+6) = 7\\ ln(x+6) = 7-x\\ e^{ln(x+6)} = e^{7-x}\\ x+6 = \frac{e^{7}}{e^x}\\ \frac{1}{x+6} = \frac{e^x}{e^{7}}\\ e^{7}= e^x(x+6)\\$$

mmm     That didn't help at all.

Apr 28, 2020
#2
+1

so is this unable to be solved? technically this a second step to my question I'm actually supposed to find the inverse of $$f(x) = 7 + x + ln(x − 6)$$where  f^-1(14). that's how I approached the question because I assumed this was the only way to solve it

Guest Apr 28, 2020
#3
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You can get the solution graphically.  It is an estimate of course.

x= 4.636

Melody  Apr 28, 2020
edited by Melody  Apr 28, 2020
#4
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Finding the inverse value, f-1(14), doesn't require you to find the complete inverse function relationship.  See what you get when you calculate the value of f(7).

I'm assuming f(x) = 7 + x + ln(x - 6)         ( i.e. with ln(x - 6) not ln(x + 6) )

Alan  Apr 28, 2020
edited by Alan  Apr 28, 2020