Logaritmen herleiden

\({}^{2}\!\log(p)+{}^{2}\!\log(5p+4)\)
\(\text{ }={}^{2}\!\log(p⋅(5p+4))\)
\(\text{ }={}^{2}\!\log(5p^2+4p)\)

\({}^{3}\!\log(4)-{}^{3}\!\log(2x+5)\)
\(\text{ }={}^{3}\!\log({4 \over 2x+5})\)

\(5+{}^{4}\!\log(x+2)\)
\(\text{ }={}^{4}\!\log(4^5)+{}^{4}\!\log(x+2)\)
\(\text{ }={}^{4}\!\log(1\,024)+{}^{4}\!\log(x+2)\)

\(\text{ }={}^{4}\!\log(1\,024⋅(x+2))\)
\(\text{ }={}^{4}\!\log(1\,024x+2\,048)\)

\(4⋅{}^{5}\!\log(3a)\)
\(\text{ }={}^{5}\!\log((3a)^4)\)

\(\text{ }={}^{5}\!\log(81a^4)\)

\({}^{3}\!\log(9)+{}^{5}\!\log(a+4)\)
\(\text{ }={}^{3}\!\log(3^2)+{}^{5}\!\log(a+4)\)
\(\text{ }=2+{}^{5}\!\log(a+4)\)

\(\text{ }={}^{5}\!\log(5^2)+{}^{5}\!\log(a+4)\)
\(\text{ }={}^{5}\!\log(25)+{}^{5}\!\log(a+4)\)

\(\text{ }={}^{5}\!\log(25⋅(a+4))\)
\(\text{ }={}^{5}\!\log(25a+100)\)

\(2⋅{}^{4}\!\log(p)+{}^{4}\!\log(3p+1)\)
\(\text{ }={}^{4}\!\log(p^2)+{}^{4}\!\log(3p+1)\)

\(\text{ }={}^{4}\!\log(p^2⋅(3p+1))\)
\(\text{ }={}^{4}\!\log(3p^3+p^2)\)