Q. 15.0( 1 Vote )

# State whether eac

(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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