From Förberedande kurs i matematik 1
The logarithm \displaystyle \lg 46 satisfies the relation
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| \displaystyle 10^{\lg 46} = 46
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and taking the natural logarithm of both sides, we obtain
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| \displaystyle \ln 10^{\lg 46 } = \ln 46\,\textrm{.}
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If we use the logarithm law, \displaystyle \lg a^b = b\cdot\lg a, on the left-hand side, the equality becomes
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| \displaystyle \lg 46\cdot\ln 10 = \ln 46\,\textrm{.}
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This shows that
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| \displaystyle \lg 46 = \frac{\ln 46}{\ln 10} = \frac{3\textrm{.}828641\,\ldots}{2\textrm{.}302585\,\ldots} = 1\textrm{.}6627578\,\ldots
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and the answer is 1.663.
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