If a,b,c are positive real numbers such that alog 7 to the base 3= 27 ; blog 11 to the - Maths - Mathematical Reasoning

Question

If a,b,c are positive real numbers such that alog 7 to the
base 3= 27 ; blog 11 to the base 7 = 49 ;
clog 25 to the base 11 = (11)1/2 The value of
[ a( log 7 to the base 3)whole squared+
b(log 11 to the base 7)whole squared+ c(log 25 to
the base 11)whole squared] equals ???

Shivam Mishra · Accepted Answer

Hi Yasra,
Please find below the solution to the asked query:

Now alog372=alog37
log37Given thatalog37=27⇒alog372=27log37=33log37Using identity nlogam=logamnalog372=3log373Now we know that ylogyx=x⇒alog372=73⇒alog372=343 ; equationiNowblog7112=blog711
log711Given thatblog711=49⇒blog7112=49log711=72log711Using identity nlogam=logamnblog7112=7log7112Now we know that ylogyx=x⇒blog7112=112⇒blog7112=121 ; equationiiNowclog11252=clog1125
log1125Given thatclog1125=11⇒clog11252=11log1125=1112log1125Using identity nlogam=logamnclog11252=11log112512Now we know that ylogyx=x⇒clog11252=25⇒clog11252=5 ; equationiiiequationi+equationii+equationiii, we getalog372+blog7112+clog11252=343+121+5⇒alog372+blog7112+clog11252=469  Answer

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If a,b,c are positive real numbers such that alog 7 to the base 3= 27 ; blog 11 to the base 7 = 49 ; clog 25 to the base 11 = (11)1/2. The value of [ a( log 7 to the base 3)whole squared+ b(log 11 to the base 7)whole squared+ c(log 25 to the base 11)whole squared] equals .... ???