CBSE Class 10 Answered
If x,y,z are real numbers satisfying the system,
log_2[(xyz-3+log_5 x)] = 5
log_3[(xyz-3+log_5 y)] = 4
log_4[(xyz-3+log_5 z)] = 4 ,
find mod(log_5 x) + mod(log_5 y) + mod(log_5 z).
(log_n k means logarithm of k to the base n)
Asked by acv27joy | 14 Dec, 2018, 02:35: PM
Expert Answer
log2 [ xyz-3 + log5 x ] = 5 or xyz-3 + log5 x = 25 = 32 or log5 x = 35 - xyz .................(1)
log3 [ xyz - 3 + log5 y ] = 4 or xyz - 3 + log5 y = 34 = 81 or log5 y = 84 - xyz ...............(2)
log4 [ xyz - 3 + log5 z ] = 4 or xyz - 3 + log5 z = 256 or log5 z = 259 - xyz .....................(3)
By adding (1)+(2)+(3), we get log5 x + log5 y + log5 z = 378 - 3xyz
Answered by Thiyagarajan K | 18 Dec, 2018, 09:08: PM
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