Answer:
[tex]\log_{100}(x^{2}) = \frac{\log_{10}(x^{2})}{\log_{10}(100)} = \frac{\log_{10}(x^{2})}{2}[/tex]
Step-by-step explanation:
We can use this expression to change the base of a logarithm from b to d.
[tex]\log_{b}(x) = \frac{\log_{d}(x)}{\log_{d}(b)}[/tex]
So, to write [tex]\log_{3}(25)[/tex] as base 10, we can use this formula.
[tex]\log_{100}(x^{2}) = \frac{\log_{10}(x^{2})}{\log_{10}(100)} = \frac{\log_{10}(x^{2})}{2}[/tex]
