SOLUTION: solve the logarithmic equation algebraically. e^x + e^-x = 4 please explain how you do this in detail. Thank you!

Question 1028474: solve the logarithmic equation algebraically.

e^x + e^-x = 4
please explain how you do this in detail. Thank you!
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
solve the logarithmic equation algebraically.

e^x + e^-x = 4
----------
Multiply thru by e^2
e^(2x) + 1 = 4e^x
e^(2x) - 4e^x + 1 = 0
Now it's quadratic in e^x.
-------------
Or,
e^x + e^-x = 4
(e^x + e^-x)/2 = 2
sinh(x) = 2
x =~ 1.443635
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

A negative exponent means one over the base with the positive exponent: Multiply through by Let Since The second way the other tutor did it, he mistakenly wrote sinh for cosh (hyperbolic functions) and got the wrong solution. It should have been cosh(x) = 2 which does gives the answer above: Edwin

RELATED QUESTIONS
how would you express the equation in logarithmic form, to this problem e^x + 3 =... (answered by Fombitz)
How do I solve for x in this inequality? Please explain in detail, because I want to be... (answered by rothauserc)
simplify the following equation: 6x-4x+x+3=10 Please explain this with detail. (answered by aseem)
How do I solve this equation for x: f(x)=xe^x+e^x Thank... (answered by macston)
Please explain in detail, how to solve this please? Solve the system of equations by... (answered by sarah_adam)
Can you please explain the steps in solving this problem in detail for me please...Thank... (answered by madhujiithcharu@yahoo.co.in)
how do you solve e^x=16? thank... (answered by edjones,solver91311)
Solve the exponential equation algebraically:... (answered by jsmallt9)
Solve the logarithmic equation algebraically approximately 3 decimal places Ln... (answered by nerdybill,stanbon)