Question Number 130242 by Raxreedoroid last updated on 23/Jan/21
$$\mathrm{Find}\:\:\:{m} \\ $$$${n}=\left({p}_{\mathrm{1}} {p}_{\mathrm{2}} \right)^{{m}} \\ $$$$\mathrm{2}{n}=\left({p}_{\mathrm{1}} ^{\mathrm{1}+{log}_{{p}_{\mathrm{1}} {p}_{\mathrm{2}} } {n}} \right)\left({p}_{\mathrm{2}} ^{\mathrm{1}+{log}_{{p}_{\mathrm{1}} {p}_{\mathrm{2}} } {n}} \right) \\ $$