Hi

In this question How I know 0,000001 = 10^-2

Is there a way ? Is there a way by Calculator ?

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- Dec 24th 2009, 02:21 AM #1

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- Dec 24th 2009, 02:32 AM #2

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- Dec 24th 2009, 03:32 AM #3

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- Dec 24th 2009, 03:51 AM #5

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- Jan 1st 2010, 10:56 AM #6

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Remember that $\displaystyle \log_a{b}=c \Longleftrightarrow\ a^{c} = b$, with $\displaystyle \log_a{b}=c$ well defined.

What it's written in yor exercise is just the aplication of the above.

Thus, you know $\displaystyle \log_b{0,0001}=-2 \Longleftrightarrow\ b^{-2}=0,0001$, but also know $\displaystyle 0,0001=10^{-4}=(10^{2})^{-2}$, because a propertie of powers says $\displaystyle (a^{b})^{c}=a^{bc}$ with $\displaystyle (a^{b})^{c}$ well defined.

Therefore, $\displaystyle b=100$

- Jan 2nd 2010, 03:37 AM #7

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