Answer:
The simplified form is [tex]\log 25[/tex]
Step-by-step explanation:
We need to simplify the given expression
Given:- [tex]log(25x^{3}+3log(\frac{1}{x})[/tex]
According to laws of logarithm : [tex]b \log a = \log a^{b}[/tex]
So, [tex]3 \log (\frac{1}{x}) = \log (\frac{1}{x^{3}})[/tex]
According to laws of logarithm : [tex]\log a + \log b = \log a\times b[/tex]
So, [tex]\log 25x^{3} + \log (\frac{1}{x})^{3} = \log 25x^{3}\times (\frac{1}{x^{3}})[/tex]
[tex]=\log (\frac{25x^{3}}{x^{3}})}[/tex]
[tex]=\log 25[/tex]
Therefore, the simplified form is [tex]\log 25[/tex]
