Logaritmen herleiden

\({}^{4}\!\log(2) + {}^{4}\!\log(5 x - 1)\)
\(\text{ } = {}^{4}\!\log(2 ⋅ (5 x - 1))\)
\(\text{ } = {}^{4}\!\log(10 x - 2)\)

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

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

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

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

\(\text{ } = {}^{3}\!\log(25 x^{2})\)

\({}^{3}\!\log(81) + {}^{2}\!\log(5 a + 1)\)
\(\text{ } = {}^{3}\!\log(3^{4}) + {}^{2}\!\log(5 a + 1)\)
\(\text{ } = 4 + {}^{2}\!\log(5 a + 1)\)

\(\text{ } = {}^{2}\!\log(2^{4}) + {}^{2}\!\log(5 a + 1)\)
\(\text{ } = {}^{2}\!\log(16) + {}^{2}\!\log(5 a + 1)\)

\(\text{ } = {}^{2}\!\log(16 ⋅ (5 a + 1))\)
\(\text{ } = {}^{2}\!\log(80 a + 16)\)

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

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