Question

Prove that: - 5 log 3−log 9=log 27

Answer 1

Answer:

5 log 3 - log 9 = log 27 [ Proved! ]

Step-by-step explanation:

We have to prove :

5 log 3 - log 9 = log 27

L.H.S. = 5 log 3 - log 9

= > log 3⁵ - log 3²

= > log ( 3⁵ / 3² )

= > log ( 3³ )

= > log 27

L.H.S.  = R.H.S.

Hence proved!

Formula used :

1. log aˣ ⇔ x log a

2. log a = log b = log ( a / b )

Answer 2

Solution -

$\sf{ \bold{ To \ Prove \ - }} \sf{ 5 log(3) - log(9) = log(27) } \\ \\ \sf{ L.H.S \ - \ 5 log(3) - log(9) } \\ \\ \sf{ R.H.S \ = \ log(27) } \\ \\ \sf{ 5 log(3) - log(9) } \\ \\ \sf{ = > 5 log(3) - log( {3}^{2} ) } \\ \\ \sf{ = > 5 log(3) - 2 log(3) } \\ \\ \sf{ = > log(3) (5 - 2) } \\ \\ \sf{ = >3 log(3) } \\ \\ \sf{ = > log( {3}^{3} ) } \\ \\ \sf{ = > log(27) } \\ \\ \sf{ \therefore{ L.H.S = R.H.S }} \\ \\ \sf{ \bold{Hence \: Proved}}$