What is the answer to 3=60+(2-60)e^{-0.001x} ?

The answer to 3=60+(2-60)e^{-0.001x} is x=-(ln(57/58))/(0.001)

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3=60+(2-60)e^{-0.001x}

3 = 60 + (2 - 60) e^{- 0.001 x}

x = - \frac{ln ( \frac{57}{58} )}{0.001}

Decimal Notation

x = 17.39174 \dots

Solution steps

3 = 60 + (2 - 60) e^{- 0.001 x}

Switch sides

60 + (2 - 60) e^{- 0.001 x} = 3

(2 - 60) e^{- 0.001 x} = - 58 e^{- 0.001 x}

60 - 58 e^{- 0.001 x} = 3

Move

60

to the right side

- 58 e^{- 0.001 x} = - 57

Divide both sides by

- 58

e^{- 0.001 x} = \frac{57}{58}

Apply exponent rules

- 0.001 x = ln (\frac{57}{58})

Solve

- 0.001 x = ln (\frac{57}{58}) : x = - \frac{ln ( \frac{57}{58} )}{0.001}

x = - \frac{ln ( \frac{57}{58} )}{0.001}

ln (1 6^{x}) = 25

(3^{x})^{2} - 2 \cdot 3^{x} - 3 = 0

(\frac{1}{9})^{x} = 729

1 6^{- 7 x} = 72

5^{2 x - 1} = 6

What is the answer to 3=60+(2-60)e^{-0.001x} ?
The answer to 3=60+(2-60)e^{-0.001x} is x=-(ln(57/58))/(0.001)