Logaritmen herleiden

\({}^{4}\!\log(5 x) + {}^{4}\!\log(x + 2)\)
\(\text{ } = {}^{4}\!\log(5 x ⋅ (x + 2))\)
\(\text{ } = {}^{4}\!\log(5 x^{2} + 10 x)\)

\({}^{5}\!\log(3 a) - {}^{5}\!\log(2 a + 1)\)
\(\text{ } = {}^{5}\!\log({3 a \over 2 a + 1})\)

\(5 + {}^{3}\!\log(a + 2)\)
\(\text{ } = {}^{3}\!\log(3^{5}) + {}^{3}\!\log(a + 2)\)
\(\text{ } = {}^{3}\!\log(243) + {}^{3}\!\log(a + 2)\)

\(\text{ } = {}^{3}\!\log(243 ⋅ (a + 2))\)
\(\text{ } = {}^{3}\!\log(243 a + 486)\)

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

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

\({}^{2}\!\log(16) + {}^{3}\!\log(p - 5)\)
\(\text{ } = {}^{2}\!\log(2^{4}) + {}^{3}\!\log(p - 5)\)
\(\text{ } = 4 + {}^{3}\!\log(p - 5)\)

\(\text{ } = {}^{3}\!\log(3^{4}) + {}^{3}\!\log(p - 5)\)
\(\text{ } = {}^{3}\!\log(81) + {}^{3}\!\log(p - 5)\)

\(\text{ } = {}^{3}\!\log(81 ⋅ (p - 5))\)
\(\text{ } = {}^{3}\!\log(81 p - 405)\)

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

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