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Popular >

e^t=1+6e^{-t}

Solution

e^{t} = 1 + 6 e^{- t}

Solution

t = ln (3)

+1

Decimal Notation

t = 1.09861 \dots

Solution steps

e^{t} = 1 + 6 e^{- t}

Apply exponent rules

e^{t} = 1 + 6 (e^{t})^{- 1}

Rewrite the equation with

e^{t} = u

u = 1 + 6 (u)^{- 1}

Solve

u = 1 + 6 u^{- 1} : u = 3, u = - 2

u = 3, u = - 2

Substitute back

u = e^{t},

solve for

t

Solve

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

Solve

e^{t} = - 2 :

No Solution for

t \in R

t = ln (3)

Popular Examples

e^{5 x} = 5 e^{x}

3^{x} = 100

3^{x-5}=27^{1-x}

3^{x - 5} = 2 7^{1 - x}

x^{log_{10}(4x)}-17=239

x^{l o g_{10} (4 x)} - 17 = 239

x e^{x} - 2 = 0

Frequently Asked Questions (FAQ)

What is the answer to e^t=1+6e^{-t} ?
The answer to e^t=1+6e^{-t} is t=ln(3)