125^1/log0,008(0,04) (номер 9)

Question

125^1/log0,008(0,04)
(номер 9)

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Answer 1

1/log(0,0008)0,04=log(0,008)0,008/log(0,008)0,04=log(04)0,008
0,04=1/25
0,008=1/125=(1/25)^3/2
log(1/25)(1/25)^3/2=3/2*log(1/25)(1/25)=3/2
125^[1/log(0,008)0,04=125^3/2=(5³)^3/2=5^4,5=625√5