If k is an integer and 0.0010101 x 10^(k) is greater than 1,000, what is the LEAST possible value of k?

Set Up:

0.0010101 x 10^(k) > 1,000.

Must I take the log on both sides to find k?

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- Dec 11th 2018, 10:05 AM #1

- Dec 11th 2018, 11:16 AM #2

- Dec 11th 2018, 03:34 PM #3

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## Re: Least Possible Value of k

I don't know if you "must" take the logarithm (especially base 10) of each side to find k, but it is geared for it.

$\displaystyle 0.0010101*10^k > 1,000$

I would isolate the exponential term first:

$\displaystyle 10^k \ > \ \dfrac{1,000}{0.0010101}$

$\displaystyle 10^k \ > 990,000.99 \ \ \ \ \ \ \ \ \ $ (rounded to two decimal places)

$\displaystyle \log_{10}(10^k) \ > \ \log_{10}(990,000.99)$

$\displaystyle k \ > \ \log_{10}(990,000.99)$

What is your conclusion from looking at the result after entering the above in a calculator/computer?

- Dec 12th 2018, 07:16 PM #4

- Dec 12th 2018, 08:03 PM #5

- Dec 13th 2018, 01:30 AM #6