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Popular >

e^x+6e^{-x}=5

Solution

e^{x} + 6 e^{- x} = 5

Solution

x = ln (3), x = ln (2)

+1

Decimal Notation

x = 1.09861 \dots, x = 0.69314 \dots

Solution steps

e^{x} + 6 e^{- x} = 5

Apply exponent rules

e^{x} + 6 (e^{x})^{- 1} = 5

Rewrite the equation with

e^{x} = u

u + 6 (u)^{- 1} = 5

Solve

u + 6 u^{- 1} = 5 : 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 : x = ln (2)

x = ln (3), x = ln (2)

Popular Examples

5^{x + 1} = \frac{1}{5}

3^{2 x} = \frac{1}{27}

7^{2 x - 3} = 5^{x}

2 7^{x} = 3

100 0^{8} = 1 0^{w}

Frequently Asked Questions (FAQ)

What is the answer to e^x+6e^{-x}=5 ?
The answer to e^x+6e^{-x}=5 is x=ln(3),x=ln(2)