a-b-c-are-real-numbers-1-lt-b-lt-c-2-lt-a-10-log-a-b-2log-b-c-5log-c-a-12-prove-that-2log-a-c-5log-c-b-10log-b-a-21-

Question Number 105269 by malwaan last updated on 27/Jul/20

a; b; c a r e r e a l n u m b e r s

1 < b < c^{2} < a^{10}

{l o g}_{a} b + 2 {l o g}_{b} c + 5 {l o g}_{c} a = 12

p r o v e t h a t

2 {l o g}_{a} c + 5 {l o g}_{c} b + 10 {l o g}_{b} a ⩾ 21