Condense: \(\ln 5 + 5\ln 3\)
$$\begin{align}
& \ln 5 + 5\ln 3 \\
& \ln 5 + \ln 3^5 \\
& \ln\left(5 \cdot 3^5\right) \\
& \ln 1215
\end{align}$$
\(\dfrac{1}{3}\ln(x + 2)^3 + \dfrac{1}{2}\left[\ln x - \ln\left(x^2 + 3x + 2\right)^2\right]
\(\ln \dfrac{\sqrt{x}}{x + 1}\)
Express the quantity as a single logarithm. 1/3 ln(x+2)^3 + 1/2[ln x- ln(x^2+ 3x +2)^2]
Ms Shaws Math Class
Condense: \(\ln 3 + \dfrac{1}{3}\ln 8\)
$$\begin{align}
& \ln 3 + \dfrac{1}{3}\ln 8 \\
& \ln 3 + \ln 8^{1 / 3} \\
& \ln 3 + \ln 2 \\
& \ln\left(3 \cdot 2\right) \\
& \ln 6
\end{align}$$
Condense: \(\log_5 7 + \log_5 3x\)
$$\begin{align}
& \log_5 7 + \log_5 3x \\
=\ & \log_5(7 \cdot 3x) \\
=\ & \log_5 21x
\end{align}$$
Condense: \(\log_4 20 + \log_4 3\)
$$\begin{align}
& \log_4 20 + \log_4 3 \\
=\ & \log_4(20 \cdot 3) \\
=\ & \log_4(60)
\end{align}$$
Condense: \(\log_2 18 - \log_2 3\)
$$\begin{align}
& \log_2 18 - \log_2 3 \\
=\ & \log_2 \dfrac{18}{3} \\
=\ & \log_2 6
\end{align}$$
Condense: \(2\log x + 3\log y + 4\log z\)
$$\begin{align}
& 2\log x + 3\log y + 4\log z \\
=\ & \log x^2 + \log y^3 + \log z^4 \\
=\ & \log x^2y^3z^4
\end{align}$$
Condense: \(\log_3 2 - 4\log_3 x\)
$$\begin{align}
& \log_3 2 - 4\log_3 x \\[0.5em]
=\ & \log_3 2 - \log_3 x^4 \\[0.5em]
=\ & \log_3 \dfrac{2}{x^4}
\end{align}$$
Condense: \(2\ln 5 - \ln 3\)
$$\begin{align}
& 2\ln 5 - \ln 3 \\
=\ & \ln 5^2 - \ln 3 \\
=\ & \ln 25 - \ln 3 \\
=\ & \ln \dfrac{25}{3}
\end{align}$$
Condense: \(\dfrac{1}{4}[\log_2(x - 1) + \log_2(x + 1) - 3\log_2 x]\)
Condense: \(2\log_3 x - 3\left[\log_3(x - 1) + 5\log z\right]\)
Condense: \(2\log_3 x - 3\left[\log_3(x - 1) + 5\log z\right]\)
Condense: \(\ln x - 4[\ln(x - 2) + \ln(x + 2)]\)
Condense: \(\ln - 4[\ln(x + 2) + \ln(x - 2)]\)
Condense: \((\log 3 - \log 4) - \log 2\)
Condense: \(\dfrac{1}{3}\left[2\ln(x + 5) - \ln x - \ln\left(x^2 - 4\right)\right]\)
Condense: \(\dfrac{1}{2}\left[\log_4(x + 1) + 2\log_4(x - 1)\right] + 6\log_4 x\)
Condense: \(\log_5 y - 4(\log_5 r + 2\log_5 t)\)
Condense: \(\dfrac{1}{3}\left[2\ln(x + 3) + \ln x - \ln\left(x^2 - 1\right)\right]\)
Condense: \(\dfrac{1}{3}\left[2\ln(x + 3) + \ln x - \ln\left(x^2 - 1\right)\right]\)
Condense: \(\dfrac{1}{2}[3\log_2 x - 2\log_2 z]\)
Condense: \(2[3\ln x - \ln(x + 1) - \ln(x - 1)]\)
Condense: \((\log 3 - \log 4) - \log 2\)
Condense: \(\dfrac{1}{3}(\log_2 x - \log_2 y)\)
Condense: \(\dfrac{1}{3}\log_4 27 - \left(2\log_4 6 - \dfrac{1}{2}\log_4 81\right)\)
Condense: \(\log_5 y - 4(\log_5 r + 2\log_5 t)\)
Condense: \(\dfrac{1}{3}\log_6 8 + 2\log_6 x + 3\log_6 y\)
Condense: \(\dfrac{1}{3}\log 3x + \dfrac{2}{3}\log 3x\)
Condense: \(\log_3 x + 2\log_3 x + 3\log_3 x\)
Condense: \(\log_2 3 + \log_2 4 - 2\log_2 x\)
Condense: \(\log_{10} x - 2\log_{10} y + 3\log_{10} z\)
Condense: \(4\log_3 x + \dfrac{1}{2}\log_3(x - 2) + \log_3 x^2\)
Condense: \(\ln(2x - 4) + \ln(3x + 2) + \ln 2\)
Condense: \(3\ln\left(x^3y\right) + 2\ln\left(yz^2\right)\)
Condense: \(\log_5 6 - \log_5 4\)
Condense: \(2\log x + 3\log y\)
Condense: \(2[3\log x + \log(x - 1)]\)
Condense: \(2\log x - 3\log y\)
Condense: \(3\ln x - 4\ln 5z - \dfrac{1}{4}\ln y\)
Condense: \(\log_8 x + \log_8 10\)
Condense: \(2\log_2(x + 3)\)
Condense: \(\log_4 x + \log_4 y\)
Condense: \(\log_{10} x - \log_{10} 3\)
Condense: \(3\log x - \log 5\)
Condense: \(6\ln x + 4\ln y\)
Condense: \(\log_3 x + 2\log_3 x - \log_3 27\)
Condense: \(3\log_3 x + 4\log_3 y - 4\log_3 z\)
Condense: \(3\log x + \dfrac{1}{3}\log y\)
Condense: \(\dfrac{1}{4}\log_3 5x\)
Condense: \(\log_5 3x\)
Condense: \(\dfrac{1}{4}\log_3 5x\)
Condense: \(\log_{10} x - 2\log_{10} y + 3\log_{10} z\)
Condense: \(\dfrac{1}{5}\log_3 x\)
Condense: \(\ln(x^2 - 3) - 2\ln x - \ln(x + 1)\)
Condense: \(\log x + \log(x^2 - 4) - \log 15 - \log(x + 2)\)
Condense: \(\log_2 x + 2\log_2 y - \log_2 4\)
Condense: \(6\log_8 2 + 2\log_8 x + 2\log_8 y\)
Condense: \(3\log_2 x + 3\log_2 x + 2\log_2 y\)
Condense: \(\ln 40 + 2\ln \dfrac{1}{2} + \ln x\)
Condense: \(3\log_4 x + \log_4 z - \log_4 3\)
Condense: \(2\log_{10} x + \log_{10} 5\)
Condense: \(\ln x + \ln 3\)
Condense: \(\log_4 7 - \log_4 10\)
Condense: \(-4\log_8 2x + \log_8(x + 1)\)
Condense: \(8\log_2 x + \dfrac{1}{2}\log_2 y - 3\log_2 z\)