a.9log 20
b.15log 48
c.2log 75
d.√5log 60
e.1/3log 24
Jawaban:
diketahui:
³log 4 = x
³log 2² = x
2•³log 2 = x
³log 2 = x/2
²log 3 = 2/x
³log 5 = y
⁵log 3 = 1/y
a.
⁹log 20
[tex] = {}^{ {3}^{2} } log \: (4 \times 5)[/tex]
[tex] = \frac{1}{2} \times {}^{3} log(4 \times 5)[/tex]
[tex] = \frac{1}{2} ( {}^{3} log \: 4 + {}^{3} log \: 5)[/tex]
[tex] = \frac{1}{2} (x + y)[/tex]
b.
[tex] {}^{15} log \: 48[/tex]
[tex] = \frac{ {}^{3}log \: 48 }{ {}^{3} log \: 15} [/tex]
[tex] = \frac{ {}^{3}log \: ( {4}^{2} \times 3) }{ {}^{3} log \: (3 \times 5)}[/tex]
[tex] = \frac{2 {}^{3}log \: 4 + {}^{3}log \: 3 }{ {}^{3}log \: 3 + {}^{3} log \: 5}[/tex]
[tex] = \frac{2x+ 1 }{ 1 + y}[/tex]
c.
[tex] {}^{2} log \: 75[/tex]
[tex] = \frac{ ^{3}log \: 75 }{ {}^{3}log \: 2 }[/tex]
[tex] = \frac{ ^{3}log \: (3 \times {5}^{2}) }{ \frac{x}{2} }[/tex]
[tex]= \frac{2( ^{3}log \: 3 + 2 \times {}^{3}log \: {5} ) }{ x }[/tex]
[tex]= \frac{2( 1 + 2y ) }{ x }[/tex]
[tex] = \frac{2 + 4y}{x} [/tex]
d.
[tex] {}^{ \sqrt{5} } log \: 60[/tex]
[tex] = {}^{ {5}^{ \frac{1}{2} } } log \: (3 \times 4 \times 5)[/tex]
[tex] = 2( {}^{5} log \: (3 \times 4 \times 5))[/tex]
[tex] = 2( \frac{ {}^{3}log \: 3 + {}^{3} log \: 4 + {}^{3}log \: 5 }{ {}^{3} log \: 5} )[/tex]
[tex] = 2( \frac{1 + x + y}{y} )[/tex]
[tex] = \frac{2 + 2x + 2y}{y} [/tex]
e.
[tex] {}^{ \frac{1}{3} } log \: 24[/tex]
[tex] = {}^{ {3}^{ - 1} } log \: ( {2}^{3} \times 3)[/tex]
[tex] = - ( {}^{3} log \: {2}^{3} + {}^{3} log \: 3)[/tex]
[tex] = - (3 \times {}^{3} log \: 2 + {}^{3} log \: 3)[/tex]
[tex] = - (3 \times \frac{x}{2} + 1)[/tex]
[tex] = - \frac{3}{2} x - 1[/tex]
[answer.2.content]
