What is the answer to 2^{1/2}=4e^{-t/(0.00001)} ?

The answer to 2^{1/2}=4e^{-t/(0.00001)} is t=(0.00003)/2 ln(2)

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2^{1/2}=4e^{-t/(0.00001)}

2^{\frac{1}{2}} = 4 e^{- \frac{t}{0.00001}}

t = \frac{0.00003}{2} ln (2)

Decimal

t = 0.00001 \dots

Solution steps

2^{\frac{1}{2}} = 4 e^{- \frac{t}{0.00001}}

Switch sides

4 e^{- \frac{t}{0.00001}} = 2^{\frac{1}{2}}

Divide both sides by

4

e^{- \frac{t}{0.00001}} = \frac{2 ^{\frac{1}{2}}}{4}

Simplify

\frac{2 ^{\frac{1}{2}}}{4} : \frac{1}{2 \cdot 2 ^{\frac{1}{2}}}

e^{- \frac{t}{0.00001}} = \frac{1}{2 \cdot 2 ^{\frac{1}{2}}}

Apply exponent rules

- \frac{t}{0.00001} = - (- \frac{- 3}{2}) ln (2)

Solve

- \frac{t}{0.00001} = - (- \frac{- 3}{2}) ln (2) : t = \frac{0.00003}{2} ln (2)

t = \frac{0.00003}{2} ln (2)

3^{20 - x} = 9

5 \times 2^{x + 1} = 15

t, A = P e^{r t}

(- 1)^{2 x} = 1

(\frac{3}{5})^{x + 1} = \frac{25}{9}

What is the answer to 2^{1/2}=4e^{-t/(0.00001)} ?
The answer to 2^{1/2}=4e^{-t/(0.00001)} is t=(0.00003)/2 ln(2)