Maka berapakah nilai dari 48 log 56
Jawab:
(ab + 3)/(a + 4)
Penjelasan dengan langkah-langkah:
48 log 56
= (3 log 56) / (3 log 48)
= (3log7 + 3log8) / (3log3 + 3log16)
= (3log7 + 3log(2^3)) / (3log3 + 3log(2^4))
= (b + (3/a)) / (1 + (4/a))
= (ab + 3) / (a + 4)
Jawaban:
aturan log:
[tex] {}^{a} log \: {b}^{n} = n \times {}^{a} log \: b[/tex]
[tex] {}^{a} log \: b = \frac{ {}^{n}log \: b }{ {}^{n} log \: a} [/tex]
[tex] {}^{2} log \: 3 = a[/tex]
[tex]maka \: {}^{3} log \: 2 = \frac{1}{a} [/tex]
[tex] {}^{48} log \: 56[/tex]
[tex] = \frac{ {}^{3} log \: 56}{ {}^{3} log48} [/tex]
[tex] = \frac{ {}^{3}log ({2}^{3} \times 7) }{ {}^{3} log( {2}^{4} \times 3) } [/tex]
[tex] = \frac{ {}^{3}log {2}^{3} + {}^{3} log7}{ {}^{3}log {2}^{4} + {}^{3} log3} [/tex]
[tex] = \frac{3( {}^{3} log2) + {}^{3}log7 }{4 ( {}^{3} log2) + {}^{3} log3} [/tex]
[tex] = \frac{ \frac{3}{a} + b }{ \frac{4}{a} + 1} [/tex]
[tex] = \frac{ \frac{3 + ab}{a} }{ \frac{4 + a}{a} } [/tex]
[tex] = \frac{3 + ab}{4 + a} [/tex]
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