What is the answer to 0.1=1-(1-1/x)^{25} ?

The answer to 0.1=1-(1-1/x)^{25} is x\approx 237.78089…

Solve for x: 0.1=1-(1-1/x)^{25}

The solution is x\approx 237.78089…

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0.1 = 1 - (1 - \frac{1}{x})^{25}

x \approx 237.78089 \dots

Solution steps

0.1 = 1 - (1 - \frac{1}{x})^{25}

Multiply by LCM

- 0.9 x^{25} = - x^{25} + 25 x^{24} - 300 x^{23} + 2300 x^{22} - 12650 x^{21} + 53130 x^{20} - 177100 x^{19} + 480700 x^{18} - 1081575 x^{17} + 2042975 x^{16} - 3268760 x^{15} + 4457400 x^{14} - 5200300 x^{13} + 5200300 x^{12} - 4457400 x^{11} + 3268760 x^{10} - 2042975 x^{9} + 1081575 x^{8} - 480700 x^{7} + 177100 x^{6} - 53130 x^{5} + 12650 x^{4} - 2300 x^{3} + 300 x^{2} - 25 x + 1

Solve

- 0.9 x^{25} = - x^{25} + 25 x^{24} - 300 x^{23} + 2300 x^{22} - 12650 x^{21} + 53130 x^{20} - 177100 x^{19} + 480700 x^{18} - 1081575 x^{17} + 2042975 x^{16} - 3268760 x^{15} + 4457400 x^{14} - 5200300 x^{13} + 5200300 x^{12} - 4457400 x^{11} + 3268760 x^{10} - 2042975 x^{9} + 1081575 x^{8} - 480700 x^{7} + 177100 x^{6} - 53130 x^{5} + 12650 x^{4} - 2300 x^{3} + 300 x^{2} - 25 x + 1 : x \approx 237.78089 \dots

x \approx 237.78089 \dots

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x \approx 237.78089 \dots

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

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

X, 4 Y = \frac{3 X}{X + 1}

\frac{x}{0.1 - x} = 7.5

\frac{4}{x} = \frac{2}{5}

What is the answer to 0.1=1-(1-1/x)^{25} ?
The answer to 0.1=1-(1-1/x)^{25} is x\approx 237.78089…
Solve for x: 0.1=1-(1-1/x)^{25}
The solution is x\approx 237.78089…