Question

31. Prove that log 5040 = 4log 2 + 2log 3 + log 5
+ log7.​

Answer 1

Answer:

Given,

Let us prove RHS

= 4 log 2 + 2 log 3 + log 5 + log 7

= log (2)⁴ + log (3)²+ log 5 + log 7

= log ( 16 x 9 x 5 x 7)

= log 5040

Let us take LHS:

Given log5040

=log(16×9×5×7)

=log 16+log 9+log 5+ log 7

=log 2⁴+log 3²+log 5+log 7

=4 log 2+2 log 3+ log 5+ log 7

(Log a^n=n log a)

HENCE, LHS=RHS.....

The answer has been explained......

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