To evaluate the expression [tex]\(\log 50 - \log 5\)[/tex], we can use the properties of logarithms. Specifically, we will use the property that relates the difference of two logarithms to the logarithm of a quotient.
The property of logarithms states:
[tex]\[ \log_a \left( \frac{x}{y} \right) = \log_a (x) - \log_a (y) \][/tex]
Here, since our expression is [tex]\(\log 50 - \log 5\)[/tex], we can apply the property as follows:
[tex]\[ \log 50 - \log 5 = \log \left( \frac{50}{5} \right) \][/tex]
Next, we simplify the fraction inside the logarithm:
[tex]\[ \frac{50}{5} = 10 \][/tex]
So, substituting back into the logarithmic expression, we get:
[tex]\[ \log \left( \frac{50}{5} \right) = \log 10 \][/tex]
We know a fundamental property of logarithms is that:
[tex]\[ \log_{10} (10) = 1 \][/tex]
Therefore:
[tex]\[ \log 10 = 1 \][/tex]
Thus, the value of the expression [tex]\(\log 50 - \log 5\)[/tex] is:
[tex]\[ 1.0 \][/tex]
