Question

log(2/3)+log(4/5)-log(8/15) find the value​

Answer 1

log(2/3)+log(4/5)-log(8/15)

log(2/3×4/5)-log(8/15)

log(8/15)-log(8/15)

=0

Answer 2

The value of the expression  log ( 2 / 3 ) + log ( 4 / 5 ) - log ( 8 / 15 ) is 0.

Given: The expression:

            log ( 2 / 3 ) + log ( 4 / 5 ) - log ( 8 / 15 )

To Find: The value of the expression:

              log ( 2 / 3 ) + log ( 4 / 5 ) - log ( 8 / 15 )

Solution:

We shall solve this numerical, by making use of the properties of logarithms which state;

           log A + log B = log (A×B)                                                   ....(1)

           log A - log B = log ( A / B )                                                ....(2)

           log 1 = 0                                                                             .....(3)

Coming to the numerical, we are given;

The expression:

            log ( 2 / 3 ) + log ( 4 / 5 ) - log ( 8 / 15 )

Applying property (1), we can say that;

        ⇒ log [( 2 / 3 ) × ( 4 / 5 )] - log ( 8 / 15 )

        ⇒ log ( 8 / 15 ) - log ( 8 / 15 )

Applying property (2), we can say that;

        ⇒ log [( 8 / 15 ) / ( 8 / 15 )]

        ⇒ log 1

Now, applying property (3), we get;

        ⇒ 0

Hence, the value of the expression  log ( 2 / 3 ) + log ( 4 / 5 ) - log ( 8 / 15 ) is 0.

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