To change \( \log_{25} 200 \) to an equivalent expression, we can use the change of base formula for logarithms, which is:
\[ \log_a b = \frac{\log_c b}{\log_c a} \]
where \( c \) can be any base, typically base 10 (common logarithm) or base \( e \) (natural logarithm).
If we choose \( c = 10 \), we can write:
\[ \log_{25} 200 = \frac{\log_{10} 200}{\log_{10} 25} \]
If we choose \( c = e \) (using natural logarithms), it becomes:
\[ \log_{25} 200 = \frac{\ln 200}{\ln 25} \]
Now, looking at your options, we can find the equivalent expression:
- \( \frac{\log 200}{\log 525} \)
- \( \frac{\log 200}{\log 25} \) - This matches what we found.
- \( \frac{\log 25}{\log 200} \)
- \( \frac{\log 200}{\ln 25} \)
The correct answer is:
\[ \frac{\log 200}{\log 25} \]
So, the equivalent expression for \( \log_{25} 200 \) is:
log200 / log25.