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-log(0.05)

 Jul 8, 2015

Best Answer 

 #1
avatar+25325 
+5

-log(0.05) ?

 

$$\small{\text{$
\begin{array}{rcl}
-\log_{10}{(0.05)} &=& \log_{10}{(1)} - \log_{10}{(0.05)} \qquad | \qquad \log_{10}{(1)} =0 \\ \\
\log_{10}{(1)} - \log_{10}{(0.05)} &=& \log_{10}{
\left(\dfrac{1}{0.05} \right)
}\\\\
&=& \log_{10}{
\left(\dfrac{100}{5} \right)
}\\\\
&=& \log_{10}{(20)}\\\\
&=& \log_{10}{(2\cdot 10)}\\\\
&=& \log_{10}{(2)}+\log_{10}{10)} \qquad | \qquad \log_{10}{(10)} =1\\\\
&=& \log_{10}{(2)}+1\\\\
&=& 1+\log_{10}{(2)}\\\\
&=& 1+0.30102999566\\\\
-\log_{10}{(0.05)} &=& 1.30102999566\\\\
\end{array}
$}}$$

 

 Jul 9, 2015
 #1
avatar+25325 
+5
Best Answer

-log(0.05) ?

 

$$\small{\text{$
\begin{array}{rcl}
-\log_{10}{(0.05)} &=& \log_{10}{(1)} - \log_{10}{(0.05)} \qquad | \qquad \log_{10}{(1)} =0 \\ \\
\log_{10}{(1)} - \log_{10}{(0.05)} &=& \log_{10}{
\left(\dfrac{1}{0.05} \right)
}\\\\
&=& \log_{10}{
\left(\dfrac{100}{5} \right)
}\\\\
&=& \log_{10}{(20)}\\\\
&=& \log_{10}{(2\cdot 10)}\\\\
&=& \log_{10}{(2)}+\log_{10}{10)} \qquad | \qquad \log_{10}{(10)} =1\\\\
&=& \log_{10}{(2)}+1\\\\
&=& 1+\log_{10}{(2)}\\\\
&=& 1+0.30102999566\\\\
-\log_{10}{(0.05)} &=& 1.30102999566\\\\
\end{array}
$}}$$

 

heureka Jul 9, 2015

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