Question

`(3)/(2) ln( {4x}^(6) ) - (4)/(5) ln( {2m}^(5) ) =`how do I do this

Answer 1

Original expression

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

The answer would be

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