Question

6. I need help with question in the attached picture!

Answer 1

Required Knowledge.

log(ab) =log(a) + log(b)

log(a/b) = log(a) -log(b)

SOLUTION

log(14/3) +log(11/5) -log(22/15)

=log((14/3)×(11/5)) -log(22/15)

=log(154/15) -log(22/15

=log( (154/15) ÷ (22/15) )

=log( (154/15) × (15/22) )

=log(154/22)

=log(77/11)

=log(7)

Hence 7 is your answer...

Hope it helps...

Regards;

Leukonov/Olegion.

Answer 2

`log( (14)/(3) ) + log( (11)/(5) ) - log( (22)/(15) ) =\log 7`

Step-by-step explanation

The given logarithmic expression is:

`log( (14)/(3) ) + log( (11)/(5) ) - log( (22)/(15) )`

We apply the product rule to the first two terms to get:

`log( (14)/(3) * (11)/(5) ) - log( (22)/(15) )`

We the apply the quotient rule:

`log( (14)/(3) * (11)/(5) / (22)/(15) )`

`log( (14)/(3) * (11)/(5) * (15)/(22) )`

We cancel out the common factors and simplify to obtain:

`log( 7 )`