Jadi, pilihan yang tepat adalah opsi (A).
Penjelasan dengan langkah-langkah:
\begin{gathered} \sf {}^{5}log \: 8 \: . \: {}^{2}log \: 30 - {}^{5} log \: 27 \: . \: {}^{3}log \: 6 \\ \begin{aligned}\sf &=\sf {}^{5}log \: {2}^{3} \: . \: {}^{2}log \: 30 - {}^{5} log \: {3}^{3} \: . \: {}^{3}log \: 6 \\ \sf &=\sf 3 \: .{}^{5}log \: \cancel{2} \: . \: {}^{\cancel{2}}log \: 30 - 3. {}^{5} log \: \cancel{3} \: . \: {}^{\cancel{3}}log \: 6\\ \sf &= \sf 3 \: .{}^{5}log \: 30 - 3 \: . {}^{5} log \: 6\\ \sf &=\sf 3 \: .\left( {}^{5}log \: \dfrac{ 30}{6} \right) \\ \sf &=\sf 3 \: . \: {}^{5}log \: 5 \\ \sf &= \sf 3 \: . \: 1\\ \sf &=\sf 3\: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \:\end{aligned}\end{gathered}
5
log8.
2
log30−
log27.
3
log6
=
log2
.
log3
=3.
log
log30−3.
=3.(
6
30
)
log5
=3.1
=3
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Jadi, pilihan yang tepat adalah opsi (A).
Penjelasan dengan langkah-langkah:
\begin{gathered} \sf {}^{5}log \: 8 \: . \: {}^{2}log \: 30 - {}^{5} log \: 27 \: . \: {}^{3}log \: 6 \\ \begin{aligned}\sf &=\sf {}^{5}log \: {2}^{3} \: . \: {}^{2}log \: 30 - {}^{5} log \: {3}^{3} \: . \: {}^{3}log \: 6 \\ \sf &=\sf 3 \: .{}^{5}log \: \cancel{2} \: . \: {}^{\cancel{2}}log \: 30 - 3. {}^{5} log \: \cancel{3} \: . \: {}^{\cancel{3}}log \: 6\\ \sf &= \sf 3 \: .{}^{5}log \: 30 - 3 \: . {}^{5} log \: 6\\ \sf &=\sf 3 \: .\left( {}^{5}log \: \dfrac{ 30}{6} \right) \\ \sf &=\sf 3 \: . \: {}^{5}log \: 5 \\ \sf &= \sf 3 \: . \: 1\\ \sf &=\sf 3\: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \:\end{aligned}\end{gathered}
5
log8.
2
log30−
5
log27.
3
log6
=
5
log2
3
.
2
log30−
5
log3
3
.
3
log6
=3.
5
log
2
.
2
log30−3.
5
log
3
.
3
log6
=3.
5
log30−3.
5
log6
=3.(
5
log
6
30
)
=3.
5
log5
=3.1
=3
Jadi, pilihan yang tepat adalah opsi (A).