Question Number 202296 by hardmath last updated on 24/Dec/23
$$\mathrm{Find}: \\ $$$$\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{log}_{\mathrm{3}} \:\left(\mathrm{log}_{\mathrm{4}} \:\mathrm{64}\right)\right)\:=\:? \\ $$
Answered by MATHEMATICSAM last updated on 24/Dec/23
$$\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{3}} \left(\mathrm{log}_{\mathrm{4}} \mathrm{64}\right)\right) \\ $$$$=\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{3}} \left(\mathrm{log}_{\mathrm{4}} \mathrm{4}^{\mathrm{3}} \right)\right) \\ $$$$=\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{3}} \mathrm{3}\right) \\ $$$$=\:\mathrm{log}_{\mathrm{2}} \mathrm{1} \\ $$$$=\:\mathrm{0} \\ $$
Commented by hardmath last updated on 24/Dec/23
$$\mathrm{thankyou}\:\mathrm{dear}\:\mathrm{ser} \\ $$