Respuesta :

Answer:

[tex]\log_414=\frac{\log_{3}14}{\log_{3}4}[/tex]

Step-by-step explanation:

We have given  [tex]log_4 14[/tex] is given we need to convert it in logarithmic base 3

Using log base change property

[tex]\log_ab=\frac{\log_cb}{\log_ca}[/tex]

So, here we have to change [tex]log_4 14[/tex]  using log base change property with base 3

where, a=4,b=14 and c=3

Substituting these values in log base change property and we get

Therefore, [tex]log_4 14=\frac{\log_{3}14}{\log_{3}4}[/tex]

abidemiokin

This can be written as a log to base 3 as shown below:

[tex]log_ab=\frac{log_314}{log_34}[/tex]

Logarithm

According to the law of logarithms

  • [tex]log_ab=\frac{log_3b}{log_3a}[/tex]

Given the logarithmic function expressed as:

[tex]log_414[/tex]

This can be written as a log to base 3 as shown below:

[tex]log_ab=\frac{log_314}{log_34}[/tex]

Note that this can be written to any base so far you are writing it as a quotient.

Learn more on logarithm here: https://brainly.com/question/25710806

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