Expand: \(\log_3 \dfrac{x^2y^3}{z}\)

$$\begin{align}
& \log_3 \dfrac{x^2y^3}{z} \\[0.75em]
=\ & \log_3 x^2y^3 - \log_3 z \\[0.75em]
=\ & \log_3 x^2 + \log_3 y^3 - \log_3 z \\[0.75em]
=\ & 2\log_3 x + 3\log_3 y - \log_3 z
\end{align}$$

Expand: \(\log_2 x^3y + \log_3 \dfrac{z^4}{x}\)

Expand: \(\log_3 7(2x - 3)^2\)

Expand: \(\log_5 \dfrac{5}{x}\)

Expand: \(\log_2 \dfrac{\sqrt{a - 1}}{9}\)

Expand: \(\log_3 \dfrac{x^2}{5}\)

Expand: \(\log \sqrt{\dfrac{2rst}{5w}}\)

Expand: \(\ln \sqrt[3]{\dfrac{x}{y}}\)

Expand: \(\log_5 \dfrac{x^2}{y^2z^3}\)

Expand: \(\log_4 \sqrt[4]{\dfrac{4r}{s^3z}}\)

Expand: \(\log_2 \dfrac{3x^2}{5y^2}\)

Expand: \(\log_2 \dfrac{\sqrt{x}y^4}{z^4}\)

Expand: \(\ln \dfrac{\sqrt[3]{x^2}y^{-4}}{z^{1 / 2}}\)

Expand: \(\log_2 16x\)

Expand: \(\log 3x^4\)

Expand: \(\ln \sqrt[4]{x^3\left(x^2 + 3\right)}\)

Expand: \(\log\left(\dfrac{2\sqrt{x}}{5}\right)^3\)

Expand: \(\log_{10} 7x^3\)

Expand: \(\ln \sqrt[4]{x^3\left(x^2 + 3\right)}\)

Expand: \(\log_2 \sqrt{4x}\)

Expand: \(\ln 10m^4n^3\)

Expand: \(\log_2 8x\)

Expand: \(\log_5 \dfrac{9}{x^3}\)

Expand: \(\ln \dfrac{12}{5}\)

Expand: \(\log\left(\dfrac{100y^3}{\sqrt[3]{x^2}}\right)\)

Expand: \(\ln \sqrt[4]{x^3\left(x^2 + 3\right)}\)

Expand: \(\ln \sqrt{\dfrac{z}{z^2 + 1}}\)

Expand: \(\log_2 \dfrac{xy^3z^2}{8}\)

Expand: \(\ln \dfrac{\sqrt{x^3}z}{4}\)

Expand: \(\log \dfrac{x^2}{3}\)

Expand: \(\ln \sqrt{\dfrac{x^2}{y^3}}\)

Expand: \(\ln\left(\dfrac{3y^2}{\sqrt{x}}\right)^4\)

Expand: \(\log_2 \dfrac{x^2y^3}{\sqrt{z}}\)

Expand: \(\log \sqrt{\dfrac{2rst}{5w}}\)

Expand: \(\ln \sqrt{ab}\)

\(\dfrac{1}{2}\ln a + \dfrac{1}{2}\ln b\)

Expand: \(\ln \sqrt[3]{\dfrac{x - 1}{x + 1}}\)

\(\dfrac{1}{3}\ln(x - 1) + \dfrac{1}{3}\ln(x + 1)\)

Expand: \(\ln \dfrac{x^2}{y^3z^4}\)

\(2\ln x - 3\ln y - 4\ln z\)

Expand: \(\ln s^4\sqrt{t\sqrt{u}}\)

\(4\ln s + \dfrac{1}{2}\ln t + \dfrac{1}{4}\ln u\)

Expand: \(\log_2 \dfrac{\sqrt{a - 1}}{9}\)

\(\dfrac{1}{2}\log_2(a - 1) - \log_2 9\)

Expand: \(\log_3 10z\)

\(\log_3 10 + \log_3 z\)

Expand: \(\log_3 4x\)

\(\log_3 4 + \log_3 x\)