What is the answer to solvefor x,3e^x=5+8e^{-x} ?

The answer to solvefor x,3e^x=5+8e^{-x} is x=ln(8/3)

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solvefor x,3e^x=5+8e^{-x}

solve for

x, 3 e^{x} = 5 + 8 e^{- x}

x = ln (\frac{8}{3})

Decimal Notation

x = 0.98082 \dots

Solution steps

3 e^{x} = 5 + 8 e^{- x}

Apply exponent rules

3 e^{x} = 5 + 8 (e^{x})^{- 1}

Rewrite the equation with

e^{x} = u

3 u = 5 + 8 (u)^{- 1}

Solve

3 u = 5 + 8 u^{- 1} : u = \frac{8}{3}, u = - 1

u = \frac{8}{3}, u = - 1

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{8}{3} : x = ln (\frac{8}{3})

Solve

e^{x} = - 1 :

No Solution for

x \in R

x = ln (\frac{8}{3})

4^{2 x + 1} = 0. 5^{3 x + 2}

9^{x + 1} = 2 7^{2 x - 5}

x, e^{x y} = 2

3^{x + 4} + 3^{x + 2} + 3^{x} = 273

What is the answer to solvefor x,3e^x=5+8e^{-x} ?
The answer to solvefor x,3e^x=5+8e^{-x} is x=ln(8/3)