To write the given logarithmic expression [tex]\( \log \left(\frac{3x}{9}\right) \)[/tex] as the sum and/or difference of logarithms, follow these steps:
1. Apply the logarithmic property for division:
The logarithm of a quotient can be expressed as the difference of the logarithms of the numerator and the denominator:
[tex]\[
\log \left(\frac{a}{b}\right) = \log(a) - \log(b)
\][/tex]
Applying this property to the given expression:
[tex]\[
\log \left(\frac{3x}{9}\right) = \log(3x) - \log(9)
\][/tex]
2. Apply the logarithmic property for multiplication:
The logarithm of a product can be expressed as the sum of the logarithms of the factors:
[tex]\[
\log(ab) = \log(a) + \log(b)
\][/tex]
Applying this property to [tex]\(\log(3x)\)[/tex]:
[tex]\[
\log(3x) = \log(3) + \log(x)
\][/tex]
Combining these results, we have:
[tex]\[
\log \left(\frac{3x}{9}\right) = \log(3) + \log(x) - \log(9)
\][/tex]
Therefore, the expression [tex]\(\log \left(\frac{3x}{9}\right)\)[/tex] written as the sum and/or difference of logarithms is:
[tex]\[
\log(3) + \log(x) - \log(9)
\][/tex]
