Question

$\frac{3}{2} ln( {4x}^{6} ) - \frac{4}{5} ln( {2m}^{5} ) =$how do I do this

Answer 1

Original expression

$\frac{3}{2}\ln 4x^6-\frac{4}{5}\ln 2m^5$$\begin{gathered} \frac{3}{2}\ln 4x^6-\frac{4}{5}\ln 2m^5 \\ \ln (4x^6)^{\frac{3}{2}}-\ln (2m^5)^{\frac{4}{5}}^{} \end{gathered}$$\begin{gathered} \ln (4^{3/2}x^{6\cdot3/2})-\ln (2^{4/5}m^{5\cdot4/5}) \\ \ln (2^{2\cdot3/2}x^9)-\ln (2^{4/5}m^4) \\ \ln (2^3x^9)-\ln (2^{4/5}m^4) \end{gathered}$$\begin{gathered} \ln (\frac{2^3x^9}{2^{4/5}m^4}) \\ \ln (\frac{2^{11/5}x^9}{m^4}) \end{gathered}$

The answer would be

$\ln (\frac{2^{\frac{11}{5}}x^9}{m^4})$