Respuesta :

[tex]\bf log_{{ a}}{{ b}}\implies \cfrac{log_{{ c}}{{ b}}}{log_{{ c}}{{ a}}}\\\\ -----------------------------\\\\ thus \\\\ log_{10}(e)=\cfrac{1}{ln(10)}\iff log_{10}(e)=\cfrac{1}{log_e(10)} \\\\ \textit{now, let us do the right-hand-side} \\\\ \cfrac{1}{log_e(10)}\implies \cfrac{1}{\frac{log_{10}(10)}{log_{10}(e)}}\implies \cfrac{\frac{1}{1}}{\frac{log_{10}(10)}{log_{10}(e)}} \\\\\\ \cfrac{1}{1}\cdot \cfrac{log_{10}(e)}{log_{10}(10)}\implies \cfrac{log_{10}(e)}{1}\implies log_{10}(e)[/tex]

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