Answer :
To solve the problem of applying the laws of logarithms to the expression [tex]\(\log_{10} \frac{18}{20}\)[/tex], we use the properties of logarithms, specifically the quotient rule.
The quotient rule for logarithms states:
[tex]\[
\log_b \left(\frac{a}{c}\right) = \log_b(a) - \log_b(c)
\][/tex]
In our given expression [tex]\(\log_{10} \frac{18}{20}\)[/tex], we can apply this rule as follows:
- Identify [tex]\(a\)[/tex] and [tex]\(c\)[/tex]: in this case, [tex]\(a = 18\)[/tex] and [tex]\(c = 20\)[/tex].
- Apply the quotient rule:
[tex]\[
\log_{10} \frac{18}{20} = \log_{10} 18 - \log_{10} 20
\][/tex]
Therefore, the correct application of the logarithm laws results in:
[tex]\(\log_{10} 18 - \log_{10} 20\)[/tex], which corresponds to option C.
So, the answer is C: [tex]\(\log_{10} 18 - \log_{10} 20\)[/tex].
The quotient rule for logarithms states:
[tex]\[
\log_b \left(\frac{a}{c}\right) = \log_b(a) - \log_b(c)
\][/tex]
In our given expression [tex]\(\log_{10} \frac{18}{20}\)[/tex], we can apply this rule as follows:
- Identify [tex]\(a\)[/tex] and [tex]\(c\)[/tex]: in this case, [tex]\(a = 18\)[/tex] and [tex]\(c = 20\)[/tex].
- Apply the quotient rule:
[tex]\[
\log_{10} \frac{18}{20} = \log_{10} 18 - \log_{10} 20
\][/tex]
Therefore, the correct application of the logarithm laws results in:
[tex]\(\log_{10} 18 - \log_{10} 20\)[/tex], which corresponds to option C.
So, the answer is C: [tex]\(\log_{10} 18 - \log_{10} 20\)[/tex].
