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Logarithms - Please Help!!!

Which of the following is equivalent to log5(m)/log15(m)?

Choose 1 answer.

A) 1/3

B) 3

C) log(3)

D) log5(15)

Sagot :

Sqdancefanidn

Answer:

  D)  log5(15)

Step-by-step explanation:

The relevant rule of logarithms is called the "change of base formula:"

  [tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}[/tex]

The logs on the right side of this equation can have any base, provided both have the same base.

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Your expression can be simplified as follows:

  [tex]\dfrac{\log_5(m)}{\log_{15}(m)}=\dfrac{\left(\dfrac{\log(m)}{\log(5)}\right)}{\left(\dfrac{\log(m)}{\log(15)}\right)}=\dfrac{\log(15)}{\log(5)}=\boxed{\log_5(15)}[/tex]

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