If logab=2 ; logbc=2 and log3c=3+log3a then (a+b+c) equals .... ?

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Please find below the solution to the asked query:

logab=2b=a2 ;equationilogbc=2c=b2  ;equationiilog3c=3+log3alog3c-log3a=3Using identity logpx-logpy=logpxy , we get,log3ca=3ca=33ca=27c=27ab2=27a By equation iia22=27a By equation iia4-27aaa3-27=0But a0 as log will be undefined.a3-27=0a3=27a=3Putting this value in equationi, we getb=32b=9Putting this value in equationii, we getc=92c=81a+b+c=3+9+81a+b+c=93

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