Natural Logarithms

Question

e9-4x = 7472

We need to express the solution in terms of natural logarithms, having both the EXACT answer and the DECIMAL APPROXIMATION.

Somehow got the decimal approximation, but not the exact answer

This is what I got:

ln((7472)-9)/-4

Answer 1

e^9-4x = 7472

 

ln(e^9-4x) = ln(7472)

 

9-4x = ln(7472)

 

  -4x = ln(7472) - 9

 

     x = (9 - ln(7472))/4

 

Note:  in your answer, if you put ( in front of ln and put parentheses around -4, the result is equivalent to my answer.   

Answer 2

if e^y=x, then ln(x)=y

therefore:

e^(9-4x)=7472

ln(7472)=9-4x

ln(7472)-9=-4x

x=[ln(7472)-9]/(-4)

 

ln(7472)=8.91891797991

x=(8.91891797991-9)/-4

x=-0.08108202/-4

x=0.020270505