Respuesta :

Logarithm properties:

[tex]\displaystyle \log_a b+\log_a c=\log_a (b\cdot c)\\\\\log_ab-\log_a c=\log_a \left( \frac{b}{c} \right)\\\\\log_{a^p}b^q= \frac{q}{p} \log_a b[/tex]

According to this, we can get:

[tex]\displaystyle a)\log_7 3+\log_7 8=\log_7 (3\cdot 8)=\log_724\\\\b) \log_89-\log_85=\log_8 \frac{9}{5}\\\\c)\log_325=2\log_35[/tex]

These questions are solved using logarithmic properties.

  • For item a, we apply that: [tex]\log_{b}{a} + \log_{b}{c} = \log_{b}{ac}[/tex]
  • For item b, we apply that: [tex]\log_{b}{a} - \log_{b}{c} = \log_{b}{\frac{a}{c}}[/tex]
  • For item c, we apply that: [tex]\log_{b}{a^c} = c\log_{b}{a}[/tex]

Doing this, we get that:

  • In item a, the missing value is 24.
  • In item b, the missing value is 5.
  • In item c, the missing value is 2.

Question a:

Logarithm of the sum, with the same base, thus:

[tex]\log_{b}{a} + \log_{b}{c} = \log_{b}{ac}[/tex]

Considering: [tex]a = 3, b = 7, c = 8[/tex], we need to find ac, so 3*8 = 24.

The missing value is 24.

Question b:

Logarithm of the difference, with the same base, thus:

[tex]\log_{b}{a} - \log_{b}{c} = \log_{b}{\frac{a}{c}}[/tex]

Considering [tex]a = 9, b = 8[/tex], and [tex]\frac{a}{c} = \frac{9}{5}[/tex], we get that [tex]c = 5[/tex]

Thus, the missing value is 5.

Question c:

Exponential property, so:

[tex]\log_{b}{a^c} = c\log_{b}{a}[/tex]

Considering: [tex]25 = 5^2[/tex]

We have that:

[tex]\log_{3}{25} = \log_{3}{5^2} = 2\log_{3}{5}[/tex]

Thus, the missing value is 2.

A similar question can be found at https://brainly.com/question/12983107

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