Solution 3.3:6b

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

Revision as of 09:22, 26 September 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}

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