What is the answer to 20=286.93(0.9738^x) ?

The answer to 20=286.93(0.9738^x) is x=(ln(2000/28693))/(ln(0.9738))

Solve for x: 20=286.93(0.9738^x)

The solution is x=(ln(2000/28693))/(ln(0.9738))

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20 = 286.93 (0.973 8^{x})

x = \frac{ln ( \frac{2000}{28693} )}{ln ( 0.9738 )}

Decimal Notation

x = 100.32288 \dots

Solution steps

20 = 286.93 (0.973 8^{x})

Switch sides

286.93 \cdot 0.973 8^{x} = 20

Multiply both sides by

100

28693 \cdot 0.973 8^{x} = 2000

Divide both sides by

28693

0.973 8^{x} = \frac{2000}{28693}

Apply exponent rules

x ln (0.9738) = ln (\frac{2000}{28693})

Solve

x ln (0.9738) = ln (\frac{2000}{28693}) : x = \frac{ln ( \frac{2000}{28693} )}{ln ( 0.9738 )}

x = \frac{ln ( \frac{2000}{28693} )}{ln ( 0.9738 )}

e^{x} = \frac{1}{10}

\frac{2 ^{x} + 1}{2 ^{x} - 1} = - 6

\frac{11}{1 + e ^{- x}} = 3

\frac{11}{1 + e ^{- x}} = 4

\frac{1}{4 ^{- x}} = \frac{1}{2}

What is the answer to 20=286.93(0.9738^x) ?
The answer to 20=286.93(0.9738^x) is x=(ln(2000/28693))/(ln(0.9738))
Solve for x: 20=286.93(0.9738^x)
The solution is x=(ln(2000/28693))/(ln(0.9738))