if log50=1.699 then what is log(100)50? with the 100 being the subscript of log

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16-03-2018
Mathematics

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if log50=1.699 then what is log(100)50? with the 100 being the subscript of log

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jdoe0001 jdoe0001 · Answer 1 · 2018-03-16T22:32:20+01:00

[tex]\bf \textit{Logarithm Change of Base Rule}\\\\ log_a b\implies \cfrac{log_c b}{log_c a} \\\\\\ \textit{Logarithm Cancellation Rules}\\\\ \boxed{log_a a^x = x}\qquad \qquad a^{log_a x}=x\\\\ -------------------------------\\\\ log_{100}(50)\implies \cfrac{log_{10}(50)}{log_{10}(100)}\implies \cfrac{log_{10}(50)}{log_{10}(10^2)}\implies \cfrac{log(50)}{2} \\\\\\ \cfrac{1.699}{2}\implies 0.8495[/tex]