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Popular >

10/3 =e^x+e^{-x}

Solution

\frac{10}{3} = e^{x} + e^{- x}

Solution

x = ln (3), x = - ln (3)

+1

Decimal Notation

x = 1.09861 \dots, x = - 1.09861 \dots

Solution steps

\frac{10}{3} = e^{x} + e^{- x}

Apply exponent rules

\frac{10}{3} = e^{x} + (e^{x})^{- 1}

Rewrite the equation with

e^{x} = u

\frac{10}{3} = u + (u)^{- 1}

Solve

\frac{10}{3} = u + u^{- 1} : u = 3, u = \frac{1}{3}

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

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 3 : x = ln (3)

Solve

e^{x} = \frac{1}{3} : x = - ln (3)

x = ln (3), x = - ln (3)

Popular Examples

f^{5} = 5^{f}

2(3.1)^x=(6.6)^x

2 (3.1)^{x} = (6.6)^{x}

m^{x + 1} = \frac{1}{2}

25^{4x+1}=5^{x-5}

2 5^{4 x + 1} = 5^{x - 5}

97 \cdot 0.9 5^{t} = 35

Frequently Asked Questions (FAQ)

What is the answer to 10/3 =e^x+e^{-x} ?
The answer to 10/3 =e^x+e^{-x} is x=ln(3),x=-ln(3)