Question

5lg 20 : 20lg5+1 =?
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Answer 1

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$\frac{5^{log20} }{20^{log5+1} } = \frac{5^{log(2^{.} 10) } }{20^{.} 20^{log5} } =$

$\frac{5^{log2 + log10} }{20^{.}(2^{.}10)^{(log5)} }= \frac{5^{log^{2+1}} }{20^{.}2^{log5} ^{.}10^{log5}}=$

$\frac{5}{20} ^{.}\frac{5^{log2}}{2^{log} ^{.}5} = \frac{1}{20} ^. \frac{5^{log5} ^{.} 5^{log2}}{5^{log5} ^. 2^{log5}} =$

$\frac{1}{20} ^. \frac{5^{log5+ log2}}{10^{log5}} = \frac{1}{20} ^. \frac{5^{log(5^. 2)}}{10^{log5}} =$

$\frac{1}{20} ^. \frac{5^{1} }{5} = \frac{1}{20}$