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Logarithmic Quotient Rule Example Archive

October 11, 2025

Problem Video
Walkthrough of logarithmic quotient rules relationship to other known rules using $log_a \left(\frac{x}{y}\right)$ as a guide. Watch
Expand $log_{2}\left(\frac{x+1}{z}\right)$ and $log_{5}\left(\frac{10}{x-2}\right)$ as much as possible using the logarithmic rules. Watch
Rewrite $log_{\pi}(x) - log_{\pi}(100)$ and $log_{11}(\pi) - log_{11}(150+z)$ as a single logarithm. Watch
Expand $ln\left(\dfrac{z}{100}\right)$ as much as possible using the logarithmic rules. Watch
Expand $log_{6}\left(\dfrac{(x+1)^4}{z^3}\right)$ as much as possible using the logarithmic rules. Watch
Expand $ln\left(\left(\dfrac{ma}{th}\right)^2\right)$ as much as possible using the logarithmic rules. Watch
Expand $log_3 \left( \dfrac{3^3\cdot (y+3)^2}{z^3 x} \right)$ as much as possible using the logarithmic rules. Watch
Expand $log_5 \left( \dfrac{5 \sqrt{x-2}}{(z^2 +1)^3 \sqrt[3]{y^5}} \right)$ as much as possible using the logarithmic rules. Watch

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