Answer :

(i) True


log5125 = 3


53 = 125


( x = logab is the logarithmic form of the exponential form ax = b)


This is true.


(ii) False




( x = logab is the logarithmic form of the exponential form ax = b)


Here


Therefore, this False.


(iii) False


Here its given log4(6 + 3) = log46 + log43


Let us consider the RHS i.e.


log46 + log43 = log4(6×3) ( according to the product rule loga(M×N) = logaM + logaN;


a,M,N are positive numbers,a≠1)


But here LHS is log4 (6 + 3)


Hence it’s False.


(iv) False


Here it’s given



Let us consider the LHS i.e.



( logaM ÷ logaN = logaM - logaN


;a,M,N are positive numbers ,a≠1)


But here the RHS is


Hence both the sides are not equal and therefore it’s False.


(v) True


Here it’s given:



( x = logab is the logarithmic form of the exponential form ax = b)



Hence LHS = RHS


Therefore this is True.


(vi) False


Here it’s given that loga (M - N) = loga M ÷ logaN


Let us consider the RHS


logaM ÷ logaN = logaM - logaN


( according to quotient rule,logaM ÷ logaN = logaM - logaN ;a,M,N are positive numbers,a≠1)


But the LHS is loga(M - N)


Therefore LHS≠RHS


Hence it’s False.


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