What is 1>100*((9/10)^n)/((9/10)^1) ?

The solution to 1>100*((9/10)^n)/((9/10)^1) is n>log_{9/10}(9/1000)

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1>100*((9/10)^n)/((9/10)^1)

1 > 100 \cdot \frac{( \frac{9}{10} ) ^{n}}{( \frac{9}{10} ) ^{1}}

n > lo g_{\frac{9}{10}} (\frac{9}{1000})

Interval Notation

(lo g_{\frac{9}{10}} (\frac{9}{1000}), \infty)

Decimal Notation

n > 44.70869 \dots

Solution steps

1 > 100 \cdot \frac{( \frac{9}{10} ) ^{n}}{( \frac{9}{10} ) ^{1}}

Switch sides

100 \cdot \frac{( \frac{9}{10} ) ^{n}}{( \frac{9}{10} ) ^{1}} < 1

Refine

100 \cdot \frac{( \frac{9}{10} ) ^{n}}{( \frac{9}{10} ) ^{1}} : \frac{1000 ( \frac{9}{10} ) ^{n}}{9}

\frac{1000 ( \frac{9}{10} ) ^{n}}{9} < 1

Multiply both sides by

9

1000 (\frac{9}{10})^{n} < 9

Divide both sides by

1000

(\frac{9}{10})^{n} < \frac{9}{1000}

Apply exponent rules

n > lo g_{\frac{9}{10}} (\frac{9}{1000})

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2 (3 x + 3) = 18

What is 1>100*((9/10)^n)/((9/10)^1) ?
The solution to 1>100*((9/10)^n)/((9/10)^1) is n>log_{9/10}(9/1000)