Lösung 3.3:6b

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Lösning 3.3:6b moved to Solution 3.3:6b: Robot: moved page)
Zeile 1: Zeile 1:
-
{{NAVCONTENT_START}}
+
The logarithm
-
<center> [[Image:3_3_6b.gif]] </center>
+
<math>\text{lg 46 }</math>
-
{{NAVCONTENT_STOP}}
+
satisfies the relation
-
[[Image:3_3_6_b.gif|center]]
+
 
 +
 
 +
<math>\text{10}^{\text{lg 46 }}=46</math>
 +
 
 +
 
 +
and taking the natural logarithm of both sides, we obtain
 +
 
 +
 
 +
<math>\ln \text{10}^{\text{lg 46 }}=\ln 46</math>
 +
 
 +
 
 +
If we use the logarithm law,
 +
<math>\lg a^{b}=b\centerdot \lg a</math>, on the left-hand side, the equality becomes
 +
 
 +
 
 +
<math>\lg 46\centerdot \ln 10=\ln 46</math>
 +
 
 +
 
 +
This shows that
 +
 
 +
 
 +
<math>\lg 46=\frac{\ln 46}{\ln 10}=\frac{3.828641}{2.302585}=1.6627578</math>
 +
 
 +
 
 +
and the answer is
 +
<math>\text{1}.\text{663}</math>.
 +
 
 +
NOTE: In order to calculate the answer on a calculator, you press
 +
 
 +
 
 +
<math>\begin{align}
 +
& \left[ 4 \right]\quad \left[ 6 \right]\quad \left[ \text{LN} \right]\quad \left[ \div \right]\quad \left[ 1 \right]\quad \left[ 0 \right]\quad \left[ \text{LN} \right]\quad \left[ = \right] \\
 +
& \quad \\
 +
\end{align}</math>

Version vom 09:22, 26. Sep. 2008

The logarithm \displaystyle \text{lg 46 } satisfies the relation


\displaystyle \text{10}^{\text{lg 46 }}=46


and taking the natural logarithm of both sides, we obtain


\displaystyle \ln \text{10}^{\text{lg 46 }}=\ln 46


If we use the logarithm law, \displaystyle \lg a^{b}=b\centerdot \lg a, on the left-hand side, the equality becomes


\displaystyle \lg 46\centerdot \ln 10=\ln 46


This shows that


\displaystyle \lg 46=\frac{\ln 46}{\ln 10}=\frac{3.828641}{2.302585}=1.6627578


and the answer is \displaystyle \text{1}.\text{663}.

NOTE: In order to calculate the answer on a calculator, you press


\displaystyle \begin{align} & \left[ 4 \right]\quad \left[ 6 \right]\quad \left[ \text{LN} \right]\quad \left[ \div \right]\quad \left[ 1 \right]\quad \left[ 0 \right]\quad \left[ \text{LN} \right]\quad \left[ = \right] \\ & \quad \\ \end{align}

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_3.3:6b“