Question

prove that 2 log 5 + log 21 - log 14 - log 6 is equal to 2 - 4 log 2​

Answer 1

Answer:

LHS=RHS. Hence proved

Answer 2

Step-by-step explanation:

L.H.S.

$= 2 log(5) + log(21) - log(14) - log(6) \\ = log( {5}^{2} ) + log(21) - log(14) - log(6)\\ = log(25) + log(21) - log(14) - log(6)$

= {log(25)+log(21)} - {log(14)+log(6)}

= (log 25•21) - (log 14•6)

= (log 525) - (log 84)

$= log( \frac{525}{84} )$

so ,

= log 6.26

= 0.795 ............. (1)

R.H.S.

= 2 - 4 log2

$= 2 - log( {2}^{4} )$

= 2 - log 16

= 2 - 1.204

= 0.795 ................. (2)

from equation (1) & (2)

L.H.S.=R.H.S

EXTRA

~ properties of log

which used above

●

$n log(x) = log( {x}^{n} )$

●

$log(x) - log(y) = log( \frac{x}{y} )$

●

$log(x) + log(y) = log(x \times y)$