SOLUTION: Show work please: solve the equation. e^x+9e^-1 --------- =3 2 a.) what is the solution in terms of natural logarithms? b.) what is the decimal approximation for the solutio

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Show work please: solve the equation. e^x+9e^-1 --------- =3 2 a.) what is the solution in terms of natural logarithms? b.) what is the decimal approximation for the solutio      Log On


   

Question 714848: Show work please: solve the equation.
e^x+9e^-1
--------- =3
2
a.) what is the solution in terms of natural logarithms?
b.) what is the decimal approximation for the solution?
note: numerator is e^x+9e^-1
denominator is 2
thank you for your help!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+%28+e%5Ex+%2B+9%2Ae%5E%28-1%29+-+1+%29+%2F+2+=+3+
++e%5Ex+%2B+9%2Ae%5E%28-1%29+-+1++=+6+
++e%5Ex+%2B+9%2Ae%5E%28-1%29+=+7+
+e%5Ex+=+7+-+9%2Ae%5E%28-1%29+
Multiply both sides by +e+
+e%5E%28+x+%2B+1+%29+=+7e+-+9+
Take the natural log of both sides
++x+%2B+1+=+ln%28+7e+-+9+%29+
(a)
+x+=+ln%28+7e+-+9+%29+-+1+
----------------------
(b)
+e+=+2.71828+
+x+=+ln%28+7%2A2.71828+-+9+%29+-+1+
+x+=+ln%28+19.02797+-+9+%29+-+1+
+x+=+ln%28+10.02797+%29+-+1+
+x+=+2.30538+-+1+
+x+=+1.30538+
----------------
check answer:
+%28+e%5Ex+%2B+9%2Ae%5E%28-1%29+-+1+%29+%2F+2+=+3+
+%28+e%5E1.30538+%2B+9%2F2.71828+-+1+%29+%2F+2+=+3+
+%28+3.689091+%2B+3.310917+-+1+%29+%2F+2+=+3+
+%28+7.0000082+-+1+%29+%2F+2+=+3+
+6.0000082+=+6+
close enough