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First, we will write the \[\log 25\] in the modified form by writing the number 25 in a different form. Therefore, we get

\[\log 25 = \log \dfrac{{100}}{4}\]

Now we will use the property of the logarithmic function i.e. \[\log a - \log b = \log \dfrac{a}{b}\].

Therefore, by using this property, we get

\[ \Rightarrow \log 25 = \log 100 - \log 4\]

We know that number 100 is the square of number 10 and number 4 is the square of number 2. Now we will write this in the above equation, we get

\[ \Rightarrow \log 25 = \log {10^2} - \log {2^2}\]

Now by using the property \[\log {a^b} = b\log a\], we get

\[ \Rightarrow \log 25 = 2\log 10 - 2\log 2\]

We know that the value of \[\log 2\] is given in the question and we know that \[\log 10 = 1\]. Therefore, we get

\[ \Rightarrow \log 25 = 2\left( 1 \right) - 2\left( {0.3010} \right)\]

Now we will solve the above equation to get the value of \[\log 25\]. Therefore, we get

\[ \Rightarrow \log 25 = 2 - 0.6020\]

\[ \Rightarrow \log 25 = 1.3980\]

Some of the basic properties of the log functions are listed below.

1.\[\log a + \log b = \log ab\]

2.\[\log {a^b} = b\log a\]

3.\[\log a - \log b = \log \dfrac{a}{b}\]

4.\[{\log _a}b = \dfrac{{\log b}}{{\log a}}\]