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Popular >

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

Solution

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

Solution

x = ln (5), x = 0

+1

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

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

Solve

u + 5 u^{- 1} = 6 : u = 5, u = 1

u = 5, u = 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 5 : x = ln (5)

Solve

e^{x} = 1 : x = 0

x = ln (5), x = 0

Popular Examples

2^{x} = 14

6 - 5^{x} = 5^{1 - x}

(9/8)^{3x+12}=1

(\frac{9}{8})^{3 x + 12} = 1

3^{2x}-4*3^x+3=0

3^{2 x} - 4 \cdot 3^{x} + 3 = 0

2.95=2.33e^{2c}

2.95 = 2.33 e^{2 c}

Frequently Asked Questions (FAQ)

What is the answer to e^x+5e^{-x}=6 ?
The answer to e^x+5e^{-x}=6 is x=ln(5),x=0