What is equivalent to ln(13 + e^6)?

Question

Which of the following is equivalent to

ln(13 + e^6)?

1) (13) + 6
2) 13 + e^6
3) 78
4) 6ln(13 + e)
5) None of the above

 

I think it's 5 because of the parenthesis you cant simplify the inner terms. I think you are not allowed to distribute the ln if I understood my teacher. Please help, I am a little foggy on how the rule applies here.  

Answer 1

The correct answer is none of the above (5).  There is no formula for the logarithm of a sum, so you cannot simplify the expression further.

 

However, note that if 

 

y = ln(13 + e⁶)

 

then 

 

e^y= 13 + e⁶

 

But 

 

e^y / e⁶ ≠ 13

 

Rather,

 

e^y - e⁶ = 13

 

 

Answer 2

You are right and the answer is none of these. The answer is actually 6+ln(13). Here is why. Let y=ln(13+e^16). Then:

e^y=13+e^6

e^y/e^6=13

e^(y-6)=13

y-6=ln(13)

y=6+ln(13)