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Popular >

e^x-1-6/(e^x)=0

Solution

e^{x} - 1 - \frac{6}{e ^{x}} = 0

Solution

x = ln (3)

+1

Decimal Notation

x = 1.09861 \dots

Solution steps

e^{x} - 1 - \frac{6}{e ^{x}} = 0

Apply exponent rules

e^{x} - 1 - 6 (e^{x})^{- 1} = 0

Rewrite the equation with

e^{x} = u

u - 1 - 6 (u)^{- 1} = 0

Solve

u - 1 - 6 u^{- 1} = 0 : u = 3, u = - 2

u = 3, u = - 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 3 : x = ln (3)

Solve

e^{x} = - 2 :

No Solution for

x \in R

x = ln (3)

Verify Solutions:

x = ln (3)

True

The solution is

x = ln (3)

Popular Examples

(5*2^{3x-1})/(4^{2x-1)}=80

\frac{5 \cdot 2 ^{3 x - 1}}{4 ^{2 x - 1}} = 80

35e^{-0.001x}=95

35 e^{- 0.001 x} = 95

3^{3x}+3^{2-x}=10*3^x

3^{3 x} + 3^{2 - x} = 10 \cdot 3^{x}

8^{2 x - 1} = 16

5^{3 x - 1} = 0.2

Frequently Asked Questions (FAQ)

What is the answer to e^x-1-6/(e^x)=0 ?
The answer to e^x-1-6/(e^x)=0 is x=ln(3)