What is the answer to solvefor x,e^x+5e^{-x}=6 ?

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

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

solve for

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

x = ln (5), x = 0

Decimal Notation

x = 1.60943 \dots, x = 0

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

n, 2^{n} = 1000000

3 \cdot 3^{\frac{x}{5}} = 1

2^{3 x} = 128

(25)^{4 x^{2} - 3 x} = \frac{1}{5}

2^{3 x} = 172

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