What is the answer to (3000)/(2+e^{2x)}=2 ?

The answer to (3000)/(2+e^{2x)}=2 is x=(ln(1498))/2

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(3000)/(2+e^{2x)}=2

\frac{3000}{2 + e ^{2 x}} = 2

x = \frac{ln ( 1498 )}{2}

Solution steps

\frac{3000}{2 + e ^{2 x}} = 2

Multiply both sides by

2 + e^{2 x}

\frac{3000}{2 + e ^{2 x}} (2 + e^{2 x}) = 2 (2 + e^{2 x})

Simplify

3000 = 2 (2 + e^{2 x})

Switch sides

2 (2 + e^{2 x}) = 3000

Divide both sides by

2

2 + e^{2 x} = 1500

Move

2

to the right side

e^{2 x} = 1498

Apply exponent rules

2 x = ln (1498)

Solve

2 x = ln (1498) : x = \frac{ln ( 1498 )}{2}

x = \frac{ln ( 1498 )}{2}

Verify Solutions:

x = \frac{ln ( 1498 )}{2}

True

The solution is

x = \frac{ln ( 1498 )}{2}

3^{4^{2^{x}}} = 8 1^{2^{6}}

10 x e^{1 - x} = 1

9^{x + 1} = 2 7^{x - 1}

4^{x - 11} = \frac{1}{16}

4^{x} + 2^{x + 1} - 1 = 0

What is the answer to (3000)/(2+e^{2x)}=2 ?
The answer to (3000)/(2+e^{2x)}=2 is x=(ln(1498))/2