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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
answered-by-expert 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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