Given ${log}_{10} 2 =^{.} 30103,$ find ${log}_{25} 200.$

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Solution

${log}_{25} 200 = \frac{log 200}{log 25} = \frac{log 2 + log 100}{log \frac{100}{4}} = \frac{log 2 + 2}{2 - 2 log 2} = \frac{2.30103}{1.39794} = 1.646$

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