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Which expression correctly shows how to rewrite log521 using a log base of 7?

log75log721
fraction numerator log subscript 7 end subscript 5 over denominator log subscript 7 end subscript 21 end fraction

​log721log75​
​, fraction numerator log subscript 7 end subscript 21 over denominator log subscript 7 end subscript 5 end fraction, ​

​log217log57​
​, fraction numerator log subscript 21 end subscript 7 over denominator log subscript 5 end subscript 7 end fraction, ​

​log57log217​

Respuesta :

Answer: log7 21 /  log7 5

I took one for the team and guessed, and got it right.

You are welcome future students.

The expression that correctly shows how to rewrite the logarithm [tex]\log_5{21}[/tex], using a logarithm of base 7, with change of base, is given as follows:

[tex]\frac{\log_7{21}}{\log_7{5}}[/tex]

How to change the base of a logarithm?

To change the base of a logarithm, a new fraction is written, in which:

  • The numerator is the logarithm of the new base of the number that the previous logarithm was calculated.
  • The denominator is the logarithm of the new base of the base of the previous logarithm was calculated.

In this problem, the logarithm that will be calculated is:

[tex]\log_5{21}[/tex]

Hence the number and the base of the logarithm are presented as follows:

  • The number is of 21.
  • The base is of 5.

With the change of the base to base 7, the numerator and the denominator of the fraction are given as follows:

  • Numerator: [tex]\log_7{21}[/tex]
  • Denominator: [tex]\log_7{5}[/tex]

Hence the simplified logarithm is presented as follows:

[tex]\frac{\log_7{21}}{\log_7{5}}[/tex]

Meaning that the correct option is the second option.

More can be learned about the change of base of a logarithm at https://brainly.com/question/25588990

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