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)=556=555=5\log _{5}\left(\dfrac{5^{3} \cdot 5^{4}}{5^{2}}\right)=\log _{5} 5^{6}=5 \log _{5} 5=5log5(5253⋅54)=log556=5log55=5.