What is the answer to 186=69+(208-69)e^{-3k} ?

The answer to 186=69+(208-69)e^{-3k} is k=-(ln(117/139))/3

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186=69+(208-69)e^{-3k}

186 = 69 + (208 - 69) e^{- 3 k}

k = - \frac{ln ( \frac{117}{139} )}{3}

Solution steps

186 = 69 + (208 - 69) e^{- 3 k}

Switch sides

69 + (208 - 69) e^{- 3 k} = 186

Subtract the numbers:

208 - 69 = 139

69 + 139 e^{- 3 k} = 186

Move

69

to the right side

139 e^{- 3 k} = 117

Divide both sides by

139

e^{- 3 k} = \frac{117}{139}

Apply exponent rules

- 3 k = ln (\frac{117}{139})

Solve

- 3 k = ln (\frac{117}{139}) : k = - \frac{ln ( \frac{117}{139} )}{3}

k = - \frac{ln ( \frac{117}{139} )}{3}

8^{10 x - 6} = 9^{7 x - 2}

25 = 75 (0.5)^{\frac{x}{9}}

0.46 = e^{- x \cdot 1000}

256 e^{2 x} = 1400

2^{x^{2} - 7 x + 16} = 16

What is the answer to 186=69+(208-69)e^{-3k} ?
The answer to 186=69+(208-69)e^{-3k} is k=-(ln(117/139))/3