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Question Number 196249 by mathlove last updated on 20/Aug/23
log_a x=30 log_b x=70 log_(ab) x=?
logax=30logbx=70logabx=?
Answered by AST last updated on 20/Aug/23
((logx)/(loga))=30;((logx)/(logb))=70⇒((log(b)+log(a))/(log(x)))=(1/(30))+(1/(70))=(1/(21)) log_(ab) x=((logx)/(log(ab)))=(1/((log(b)+log(a))/(log(x))))=21
logxloga=30;logxlogb=70⇒log(b)+log(a)log(x)=130+170=121logabx=logxlog(ab)=1log(b)+log(a)log(x)=21

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