Verified Answer :

Logarithm properties:

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

According to this, we can get:

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

These questions are solved using logarithmic properties.

  • For item a, we apply that: \(\log_{b}{a} + \log_{b}{c} = \log_{b}{ac}\)
  • For item b, we apply that: \(\log_{b}{a} - \log_{b}{c} = \log_{b}{\frac{a}{c}}\)
  • For item c, we apply that: \(\log_{b}{a^c} = c\log_{b}{a}\)

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:

\(\log_{b}{a} + \log_{b}{c} = \log_{b}{ac}\)

Considering: \(a = 3, b = 7, c = 8\), 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:

\(\log_{b}{a} - \log_{b}{c} = \log_{b}{\frac{a}{c}}\)

Considering \(a = 9, b = 8\), and \(\frac{a}{c} = \frac{9}{5}\), we get that \(c = 5\)

Thus, the missing value is 5.

Question c:

Exponential property, so:

\(\log_{b}{a^c} = c\log_{b}{a}\)

Considering: \(25 = 5^2\)

We have that:

\(\log_{3}{25} = \log_{3}{5^2} = 2\log_{3}{5}\)

Thus, the missing value is 2.

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

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