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Popular >

e^x+4/(e^x)=4

Solution

e^{x} + \frac{4}{e ^{x}} = 4

Solution

x = ln (2)

+1

Decimal Notation

x = 0.69314 \dots

Solution steps

e^{x} + \frac{4}{e ^{x}} = 4

Apply exponent rules

e^{x} + 4 (e^{x})^{- 1} = 4

Rewrite the equation with

e^{x} = u

u + 4 (u)^{- 1} = 4

Solve

u + 4 u^{- 1} = 4 : u = 2

u = 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 2 : x = ln (2)

x = ln (2)

Verify Solutions:

x = ln (2)

True

The solution is

x = ln (2)

Popular Examples

5 (2^{3 x}) = 9

5^{x} = 15

32 = 2^{x}

36e^{5-z}-6^{2z}=0

36 e^{5 - z} - 6^{2 z} = 0

4^{x} = \frac{1}{64}

Frequently Asked Questions (FAQ)

What is the answer to e^x+4/(e^x)=4 ?
The answer to e^x+4/(e^x)=4 is x=ln(2)