宇宙文明
log 10  { e x ( Y − Y 0 ) } = log e  e x ( Y − Y 0 ) log e  10 = x ( Y − Y 0 ) log e  10 {\displaystyle \log _{10}\{e^{x(Y-Y_{0})}\}={\frac {\log _{e}e^{x(Y-Y_{0})}}{\log _{e}10}}={\frac {x(Y-Y_{0})}{\log _{e}10}}} なので
K p = log 10  W 0 + x ( Y − Y 0 ) log e  10 − 6 10 = ( x 10 log e  10 ) ⋅ Y + ( log e  10 log 10  W 0 − x Y 0 − 6 l o g e 10 10 log e  10 ) {\displaystyle K_{p}={\frac {\log _{10}W_{0}+{\frac {x(Y-Y_{0})}{\log _{e}10}}-6}{10}}={\biggl (}{\frac {x}{10\log _{e}10}}{\biggr )}\centerdot Y+\left({\frac {\log _{e}10\log _{10}W_{0}-xY_{0}-6log_{e}10}{10\log _{e}10}}\right)}
再び、底の変換公式を適用して
∴ K p = ( x 10 log e  10 ) ⋅ Y + { log 10  ( W 0 − e ) − x Y 0 − 6 l o g e 10 10 log e  10 } {\displaystyle K_{p}={\biggl (}{\frac {x}{10\log _{e}10}}{\biggr )}\centerdot Y+{\biggl \{}{\frac {\log _{10}(W_{0}-e)-xY_{0}-6log_{e}10}{10\log _{e}10}}{\biggl \}}}