Herleid tot één logaritme.
1p
\({}^{4}\!\log(2) + {}^{4}\!\log(5 x + 1)\)
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\({}^{4}\!\log(2) + {}^{4}\!\log(5 x + 1)\)
\(\text{ } = {}^{4}\!\log(2 ⋅ (5 x + 1))\)
\(\text{ } = {}^{4}\!\log(10 x + 2)\)
1p
Herleid tot één logaritme.
1p
\({}^{4}\!\log(2 x) - {}^{4}\!\log(x + 5)\)
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\({}^{4}\!\log(2 x) - {}^{4}\!\log(x + 5)\)
\(\text{ } = {}^{4}\!\log({2 x \over x + 5})\)
1p
Herleid tot één logaritme.
2p
\(3 + {}^{2}\!\log(x - 5)\)
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\(3 + {}^{2}\!\log(x - 5)\)
\(\text{ } = {}^{2}\!\log(2^{3}) + {}^{2}\!\log(x - 5)\)
\(\text{ } = {}^{2}\!\log(8) + {}^{2}\!\log(x - 5)\)
1p
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\(\text{ } = {}^{2}\!\log(8 ⋅ (x - 5))\)
\(\text{ } = {}^{2}\!\log(8 x - 40)\)
1p
Herleid tot één logaritme.
2p
\(3 ⋅ {}^{2}\!\log(5 a)\)
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\(3 ⋅ {}^{2}\!\log(5 a)\)
\(\text{ } = {}^{2}\!\log((5 a)^{3})\)
1p
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\(\text{ } = {}^{2}\!\log(125 a^{3})\)
1p
Herleid tot één logaritme.
3p
\({}^{5}\!\log(25) + {}^{3}\!\log(4 x - 1)\)
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\({}^{5}\!\log(25) + {}^{3}\!\log(4 x - 1)\)
\(\text{ } = {}^{5}\!\log(5^{2}) + {}^{3}\!\log(4 x - 1)\)
\(\text{ } = 2 + {}^{3}\!\log(4 x - 1)\)
1p
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\(\text{ } = {}^{3}\!\log(3^{2}) + {}^{3}\!\log(4 x - 1)\)
\(\text{ } = {}^{3}\!\log(9) + {}^{3}\!\log(4 x - 1)\)
1p
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\(\text{ } = {}^{3}\!\log(9 ⋅ (4 x - 1))\)
\(\text{ } = {}^{3}\!\log(36 x - 9)\)
1p
Herleid tot één logaritme.
2p
\(5 ⋅ {}^{2}\!\log(p) + {}^{2}\!\log(4 p + 1)\)
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\(5 ⋅ {}^{2}\!\log(p) + {}^{2}\!\log(4 p + 1)\)
\(\text{ } = {}^{2}\!\log(p^{5}) + {}^{2}\!\log(4 p + 1)\)
1p
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\(\text{ } = {}^{2}\!\log(p^{5} ⋅ (4 p + 1))\)
\(\text{ } = {}^{2}\!\log(4 p^{6} + p^{5})\)
1p