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Popular >

1000(9/10)^n<0.01

Solution

1000 (\frac{9}{10})^{n} < 0.01

Solution

n > lo g_{\frac{9}{10}} (\frac{0.01}{1000})

+2

Interval Notation

(lo g_{\frac{9}{10}} (\frac{0.01}{1000}), \infty)

Decimal Notation

n > 109.27172 \dots

Solution steps

1000 (\frac{9}{10})^{n} < 0.01

Divide both sides by

1000

\frac{1000 ( \frac{9}{10} ) ^{n}}{1000} < \frac{0.01}{1000}

Simplify

(\frac{9}{10})^{n} < \frac{0.01}{1000}

Apply exponent rules

n > lo g_{\frac{9}{10}} (\frac{0.01}{1000})

Popular Examples

factor x^5+5x^2-4x^3-20 factor

x^{5} + 5 x^{2} - 4 x^{3} - 20

2 (0) + y = 4

20 + x + 2 x = 100

2 (6 x + x^{2}) = - 14

simplify 1/(n^3)*((n+1)(2n+1))/6 simplify

\frac{1}{n ^{3}} \cdot \frac{( n + 1 ) ( 2 n + 1 )}{6}

Frequently Asked Questions (FAQ)

What is 1000(9/10)^n<0.01 ?
The solution to 1000(9/10)^n<0.01 is n>log_{9/10}((0.01)/(1000))