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Find-log-2-log-3-log-4-64-




Question Number 202296 by hardmath last updated on 24/Dec/23
Find:  log_2  (log_3  (log_4  64)) = ?
$$\mathrm{Find}: \\ $$$$\mathrm{log}_{\mathrm{2}} \:\left(\mathrm{log}_{\mathrm{3}} \:\left(\mathrm{log}_{\mathrm{4}} \:\mathrm{64}\right)\right)\:=\:? \\ $$
Answered by MATHEMATICSAM last updated on 24/Dec/23
log_2 (log_3 (log_4 64))  = log_2 (log_3 (log_4 4^3 ))  = log_2 (log_3 3)  = log_2 1  = 0
$$\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{3}} \left(\mathrm{log}_{\mathrm{4}} \mathrm{64}\right)\right) \\ $$$$=\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{3}} \left(\mathrm{log}_{\mathrm{4}} \mathrm{4}^{\mathrm{3}} \right)\right) \\ $$$$=\:\mathrm{log}_{\mathrm{2}} \left(\mathrm{log}_{\mathrm{3}} \mathrm{3}\right) \\ $$$$=\:\mathrm{log}_{\mathrm{2}} \mathrm{1} \\ $$$$=\:\mathrm{0} \\ $$
Commented by hardmath last updated on 24/Dec/23
thankyou dear ser
$$\mathrm{thankyou}\:\mathrm{dear}\:\mathrm{ser} \\ $$

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