if log45=a and log56=b, then log32 isequal to: (i) 1/ (2a+1) (ii) 1/(2b+1) (iii)2ab+1 (iv) 1/(2ab-1) - Maths - Limits and Derivatives

Question

if log45=a and log56=b, then log32
isequal to:
(i) 1/ (2a+1)
(ii) 1/(2b+1)
(iii)2ab+1
(iv) 1/(2ab-1)

Rajat Sethi · Accepted Answer

log45=a;log56=bNow,a×b=log45×log56⇒ab=log5log4×log6log5   [ Since,logab=logbloga]⇒ab=log46⇒ab=12log26=12log2(2×3)⇒ab=12(log22+log23)⇒2ab=1+log23⇒log23=2ab-1⇒log32=12ab-1

if log45=a and log56=b, then log32 isequal to:(i) 1/ (2a+1)(ii) 1/(2b+1)(iii)2ab+1(iv) 1/(2ab-1)

if log₄5=a and log₅6=b, then log₃2 isequal to:
(i) 1/ (2a+1)
(ii) 1/(2b+1)
(iii)2ab+1
(iv) 1/(2ab-1)