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

ANSWER

$log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) =\log 7$

EXPLANATION

The given logarithmic expression is:

$log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} )$

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

$log( \frac{14}{3} \times \frac{11}{5} ) - log( \frac{22}{15} )$

We the apply the quotient rule:

$log( \frac{14}{3} \times \frac{11}{5} \div \frac{22}{15} )$

$log( \frac{14}{3} \times \frac{11}{5} \times \frac{15}{22} )$

We cancel out the common factors and simplify to obtain:

$log( 7 )$