Problem: The value of 5(125)(625)25\log _{5} \dfrac{(125)(625)}{25}log525(125)(625) is equal to
Answer Choices:
A. 725725725 B. 666 C. 312531253125 D. 555 E. none of these answers
Solution:
5(53⋅5452)=5(53+4−2)=5(55)=55(5)=5(1)=5\begin{aligned} \log_{5}\left(\frac{5^{3} \cdot 5^{4}}{5^{2}}\right) &= \log_{5}\left(5^{3+4-2}\right) \\ &= \log_{5}(5^{5}) \\ &= 5\log_{5}(5) \\ &= 5(1) \\ &= \boxed{5} \end{aligned} log5(5253⋅54)=log5(53+4−2)=log5(55)=5log5(5)=5(1)=5