Question

Type the correct answer in the box.

$log\frac{14}{3}+log\frac{11}{5}-log\frac{22}{15} = log$ (correct answer goes here)

Answer 1

Answer:

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

7 goes into the box

Answer 2

Answer:

log(7)

Step-by-step explanation:

Product Rule:

Let m and n be two numbers, if they share a common base, following law applies:

• $\sf log_{}(m) \: + log(n ) = log(m \times n) = log(mn)$

Quotient Rule:

Let m and n be two numbers, if they share a common base, following law applies:

• $\sf log( \dfrac{m}{n}) \: = log(m) - log(n)$

Question:

$\sf log\dfrac{14}{3}+log\dfrac{11}{5}-log\dfrac{22}{15}$

Solution:

Apply Product law to log(14/3) and log(11/5):

• $\sf log( \dfrac{14}{3} \times \dfrac{11}{5} ) - log( \dfrac{22}{15} )$

Now apply quotient law to log(22/15):

• $\sf log( \dfrac{14 \times 11}{15} \: \div \dfrac{22}{15} )$

Applying Reciprocal Rule of division:

• $\sf log( \dfrac{14 \times 11}{15} \: \times \dfrac{15}{22} )$

Cancel wherever required:(15 and 15 cancel, 11 and 22 goes to 1/2)

• $\sf log( \dfrac{14}{2} )$

• $\sf log(7)$

Remember: Every term shares a common base of 10.