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Type the correct answer in the box.

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

Type the correct answer in the box texlogfrac143logfrac115logfrac2215 logtex correct answer goes here class=

Respuesta :

Answer:

[tex] log \: \frac{14}{3} + log \: \frac{11}{5} - log \: \frac{22}{15} = log( (\frac{14}{3}) ( \frac{11}{5}) ( \frac{15}{22} )) = log \: 7 [/tex]

7 goes into the box

MisterBrian

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:

  • [tex]\sf log_{}(m) \: + log(n ) = log(m \times n) = log(mn)[/tex]

Quotient Rule:

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

  • [tex]\sf log( \dfrac{m}{n}) \: = log(m) - log(n)[/tex]

Question:

[tex]\sf log\dfrac{14}{3}+log\dfrac{11}{5}-log\dfrac{22}{15}[/tex]

Solution:

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

  • [tex]\sf log( \dfrac{14}{3} \times \dfrac{11}{5} ) - log( \dfrac{22}{15} ) [/tex]

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

  • [tex] \sf log( \dfrac{14 \times 11}{15} \: \div \dfrac{22}{15} ) [/tex]

Applying Reciprocal Rule of division:

  • [tex]\sf log( \dfrac{14 \times 11}{15} \: \times \dfrac{15}{22} ) [/tex]

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

  • [tex]\sf log( \dfrac{14}{2} )[/tex]

  • [tex]\sf log(7)[/tex]

Remember: Every term shares a common base of 10.

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