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Logarithmic Power Rule Example Archive

October 11, 2025

Problem Video
Move the power inside $log_{4}((x+1)^3)$ to the outside of the logarithm using the power rule. Watch
Move the power inside $log_{5}(x^{10})$, $log_{12}((x+5)^y)$, and $ln(y^z)$ to the outside of the logarithm using the power rule. Watch
Move the number multiplied by the logarithm in $15 log_{10}(y)$ to the inside of the logarithm. Watch
Move the number multiplied by the logarithm in $40 log_2(x)$, $15 log_{10}(x+y+z)$, and $12 ln(y)$ to the inside of the logarithm. Watch
Expand $log_{5}(z^7)$ as much as possible using the logarithmic rules. Watch
Expand $log_{2}(xz^5)$ 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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