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Popular >

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

Solution

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

Solution

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

+1

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

100-98y+980(1-e^{-0.1y})=0

100 - 98 y + 980 (1 - e^{- 0.1 y}) = 0

4 e^{2 x} = 0

9*2^{x-1}=2*3^x

9 \cdot 2^{x - 1} = 2 \cdot 3^{x}

2^{(x^2-10x+25)}-5=11

2^{(x^{2} - 10 x + 25)} - 5 = 11

3^{x + 1} + 5 = 2^{5}

Frequently Asked Questions (FAQ)

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