Question Number 186305 by mustafazaheen last updated on 03/Feb/23
$$\mathrm{log}\:\left(\frac{\mathrm{3}.\bar {\mathrm{2}}}{\mathrm{3}.\bar {\mathrm{1}}}\right)\:\:\:\:\:\:\:{find}\:\mathrm{Characteristic}? \\ $$
Commented by MJS_new last updated on 03/Feb/23
$$\frac{\mathrm{3}+\frac{\mathrm{2}}{\mathrm{9}}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{9}}}=\frac{\mathrm{29}}{\mathrm{28}}=\frac{\mathrm{29}}{\mathrm{2}^{\mathrm{2}} \mathrm{7}} \\ $$$$\mathrm{log}\:\frac{\mathrm{29}}{\mathrm{2}^{\mathrm{2}} \mathrm{7}}\:=\mathrm{log}\:\mathrm{29}\:−\mathrm{log}\:\mathrm{7}\:−\mathrm{2log2} \\ $$$$\mathrm{what}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{with}\:“\mathrm{characteristic}''? \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{an}\:\mathrm{irrational}\:\mathrm{number} \\ $$
Commented by ajfour last updated on 03/Feb/23
$${I}\:{think}\:{characteristic}\:{is}\:\left\{\:\right\}. \\ $$$$\left\{\mathrm{2}.\mathrm{13}\right\}=\mathrm{2}\:\:,\:\:\left\{−\mathrm{2}.\mathrm{13}\right\}=−\mathrm{3} \\ $$
Commented by MJS_new last updated on 03/Feb/23
$$\mathrm{if}\:\mathrm{so}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{is}\:\mathrm{0} \\ $$$$\mathrm{log}\:\mathrm{1}\:<\mathrm{log}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{28}}\right)\:<\mathrm{log}\:\mathrm{e} \\ $$$$\mathrm{0}<\mathrm{log}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{28}}\right)\:<\mathrm{1} \\ $$