SOLUTION: I'm having trouble with this problem. Thanks for your help. Solve. Express x as a logarithm if necessary. e^(x)+e^(-x)=4

Question 484241: I'm having trouble with this problem. Thanks for your help.
Solve. Express x as a logarithm if necessary.
e^(x)+e^(-x)=4
Found 2 solutions by jim_thompson5910, chessace:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Rewrite as

Multiply EVERY term by the LCD to clear out the fractions.

Get everything to one side.

Rearrange the terms.

Rewrite the first term

Replace EVERY copy of with 'z' (so )

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "z":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify the square root

Break up the fraction.

Reduce.

or Break up the expression.

So the solutions are or

But remember, we said that

So or

Now convert to logarithmic form to get

or

So the solutions are

or

Answer by chessace(471) (Show Source): You can put this solution on YOUR website!
Let z=
Note that =
So we have z + 1/z = 4
*z: + 1 = 4z
- 4z +1 =0
z =
z =
= = 2 * sqrt(3)
z =
Ln(z) = x (natural log base e)
So x =

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