Question Number 227878 by hardmath last updated on 23/Feb/26
$$\mathrm{Find}: \\ $$$$\mathrm{5}^{\left(\boldsymbol{\mathrm{log}}_{\mathrm{5}} \mathrm{3}\right)^{\mathrm{144}} } \:\:=\:\:? \\ $$
Commented by mr W last updated on 23/Feb/26
$${it}'{s}\:{not}\:{a}\:{question}\:{with}\:{much}\:{sense}! \\ $$$$\mathrm{log}_{\mathrm{5}} \:\mathrm{3}\:>\mathrm{0}\:{but}\:<\mathrm{1} \\ $$$$\Rightarrow\left(\mathrm{log}_{\mathrm{5}} \:\mathrm{3}\right)^{\mathrm{144}} \:\sim\mathrm{0} \\ $$$$\Rightarrow\mathrm{5}^{\left(\mathrm{log}_{\mathrm{5}} \:\mathrm{3}\right)^{\mathrm{144}} } \sim\:\mathrm{5}^{\mathrm{0}} \sim\mathrm{1} \\ $$
Commented by hardmath last updated on 23/Feb/26
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{professor} \\ $$
Commented by fantastic2 last updated on 23/Feb/26
Commented by hardmath last updated on 26/Feb/26
$$\mathrm{5}^{\left(\boldsymbol{\mathrm{log}}_{\mathrm{5}} \mathrm{3}\right)^{\boldsymbol{\mathrm{log}}_{\mathrm{3}} \mathrm{144}} } \:\:=\:\:\:\mathrm{12}.? \\ $$