[tex]\text{ 4}\log _{\{10\}}10\text{ - }\log _{\{10\}}y[/tex]Explanation:
The quotient property of logarithms states that the logarithm of quotient is the same as the difference of the logarithms
[tex]\log \frac{10,000}{y}\text{ }[/tex][tex]\text{Difference of the logarithm = = log}10,000\text{ - log y}[/tex][tex]\begin{gathered} \log \frac{10,000}{y}\text{ = log}10,000\text{ - log y} \\ we\text{ can stop here or continue} \\ \text{Since = }log=\log _{\mleft\{10\mright\}} \\ \text{log}10,000\text{ - log y = }\log _{\{10\}}10,000\text{ - }\log _{\{10\}}y \\ =\text{ }\log _{\{10\}}10^4\text{ - }\log _{\{10\}}\text{ y} \\ =\text{ 4}\log _{\{10\}}10\text{ - }\log _{\{10\}}y \end{gathered}[/tex][tex]\begin{gathered} we\text{ were asked to simplify: } \\ \text{the answer:} \\ \text{ 4}\log _{\{10\}}10\text{ - }\log _{\{10\}}y \end{gathered}[/tex]
