Solution 3.3:6b
From Förberedande kurs i matematik 1
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| - | {{ | + | The logarithm <math>\lg 46</math> satisfies the relation |
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| - | {{ | + | {{Displayed math||<math>10^{\lg 46} = 46</math>}} |
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| + | and taking the natural logarithm of both sides, we obtain | ||
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| + | {{Displayed math||<math>\ln 10^{\lg 46 } = \ln 46\,\textrm{.}</math>}} | ||
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| + | If we use the logarithm law, <math>\lg a^b = b\cdot\lg a</math>, on the left-hand side, the equality becomes | ||
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| + | {{Displayed math||<math>\lg 46\cdot\ln 10 = \ln 46\,\textrm{.}</math>}} | ||
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| + | This shows that | ||
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| + | {{Displayed math||<math>\lg 46 = \frac{\ln 46}{\ln 10} = \frac{3\textrm{.}828641\,\ldots}{2\textrm{.}302585\,\ldots} = 1\textrm{.}6627578\,\ldots</math>}} | ||
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| + | and the answer is 1.663. | ||
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| + | Note: In order to calculate the answer on the calculator, you press | ||
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| + | {| border="1" cellpadding="3" cellspacing="0" | ||
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| + | {| border="1" cellpadding="3" cellspacing="0" | ||
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| + | {| border="1" cellpadding="3" cellspacing="0" | ||
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Current revision
The logarithm \displaystyle \lg 46 satisfies the relation
| \displaystyle 10^{\lg 46} = 46 |
and taking the natural logarithm of both sides, we obtain
| \displaystyle \ln 10^{\lg 46 } = \ln 46\,\textrm{.} |
If we use the logarithm law, \displaystyle \lg a^b = b\cdot\lg a, on the left-hand side, the equality becomes
| \displaystyle \lg 46\cdot\ln 10 = \ln 46\,\textrm{.} |
This shows that
| \displaystyle \lg 46 = \frac{\ln 46}{\ln 10} = \frac{3\textrm{.}828641\,\ldots}{2\textrm{.}302585\,\ldots} = 1\textrm{.}6627578\,\ldots |
and the answer is 1.663.
Note: In order to calculate the answer on the calculator, you press
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