Question

log base 5 1/625 as an exponent

Answer 1

\(\Large\color{black}{ \bf log_5(\frac{1}{625})=log_5(\frac{1^4}{5^4}) =log_5(\frac{1}{5}) ^4 }\)

\(\Large\color{black}{ \bf log_5(\frac{1}{5}) ^4= 4~log_5(\frac{1}{5})=4log_5(1 \div5) }\)


\(\large\color{black}{ \bf 4log_5(1 \div5) =4(log_51-log_55)=4log_51-4log_55}\)

\(\large\color{black}{ \bf 4log_51-4log_55=4(0)-4(1)=0-4=-4}\)