Question Number 192426 by mathlove last updated on 17/May/23
$${log}\left(−\mathrm{10}\right)\left(−\mathrm{10}\right)=? \\ $$
Answered by Frix last updated on 18/May/23
$$\mathrm{Unclear}: \\ $$$$\mathrm{log}\:\left({a}\right)\:\left({a}\right)\:=\left({a}\right)\mathrm{log}\:\left({a}\right) \\ $$$$−\mathrm{10}\:\mathrm{log}\:\left(−\mathrm{10}\right)\:=−\mathrm{10log}\:\left(\mathrm{10e}^{\mathrm{i}\pi} \right) \\ $$$$\mathrm{Or}\:\mathrm{do}\:\mathrm{you}\:\mathrm{mean}: \\ $$$$\mathrm{log}\:\left(\left({a}\right)\left({a}\right)\right) \\ $$$$\mathrm{log}\:\left(\left(−\mathrm{10}\right)\left(−\mathrm{10}\right)\right)\:=\mathrm{log}\:\left(\mathrm{100}\right) \\ $$$$\mathrm{Is}\:``\mathrm{log}''\:=\:\mathrm{log}_{\mathrm{10}} \:\mathrm{or}\:\mathrm{ln}? \\ $$
Commented by mathlove last updated on 18/May/23
$${log}_{\mathrm{10}} \left(\left(−\mathrm{10}\right)\left(−\mathrm{10}\right)\right) \\ $$
Commented by Frix last updated on 18/May/23
$$\mathrm{log}_{\mathrm{10}} \:\left(\left(−\mathrm{10}\right)\left(−\mathrm{10}\right)\right)\:=\mathrm{log}_{\mathrm{10}} \:\mathrm{100}\:=\mathrm{2} \\ $$