What is the answer to 4e^x=25-25e^{-x} ?

The answer to 4e^x=25-25e^{-x} is x=ln(5),x=ln(5/4)

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4e^x=25-25e^{-x}

4 e^{x} = 25 - 25 e^{- x}

x = ln (5), x = ln (\frac{5}{4})

Decimal Notation

x = 1.60943 \dots, x = 0.22314 \dots

Solution steps

4 e^{x} = 25 - 25 e^{- x}

Apply exponent rules

4 e^{x} = 25 - 25 (e^{x})^{- 1}

Rewrite the equation with

e^{x} = u

4 u = 25 - 25 (u)^{- 1}

Solve

4 u = 25 - 25 u^{- 1} : u = 5, u = \frac{5}{4}

u = 5, u = \frac{5}{4}

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = \frac{5}{4} : x = ln (\frac{5}{4})

x = ln (5), x = ln (\frac{5}{4})

e^{x} = 2

e^{x} = 1

2^{n - 1} = 64

2^{x + 3} - 2^{x} = 7 \cdot 2^{x}

What is the answer to 4e^x=25-25e^{-x} ?
The answer to 4e^x=25-25e^{-x} is x=ln(5),x=ln(5/4)