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[tex]\begin{aligned} \sf 3^n &= \sf 54 \\ n &= \sf log_3(54) \\&= \sf log_3(27 \times 2) \\&= \sf log_3(27) + log_3(2) \\&= \sf log_3(3^3) + log_3(2) \\&= \sf 3 + log_3(2) \end{aligned}[/tex]
[tex]\begin{aligned} \sf 9^{n - 2} &= \sf 9^{3 + log_3(2)-2} \\&= \sf 9^3 \times 9^{log_3(2)} \times 9^{-2} \\&= \sf 9^3 \times (3^2)^{log_3(2)} \times 9^{-2} \\&= \sf 9^3 \times (3)^{2log_3(2)} \times 9^{-2} \\&= \sf 9^3 \times (3)^{log_3(2^2)} \times 9^{-2} \\&= \sf 9^3 \times 2^2 \times 9^{-2} \\&= 9^{3-2} \times 2^2 \\&=\sf 9 \times 4 \\&= \boxed{\bold{\underline{ \sf36}}} \end{aligned}[/tex]
[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at | 02 - 07 - 2023}}[/tex]
Jawab:
Cukup ingat konsep eksponen ini :
[tex]1. a^{m-n} = \frac{a^{m} }{a^{n} } \\2. a^{mn} = (a^{m}) ^{n} = (a^{n}) ^{m}[/tex]
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Eksponen dan Logaritma
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[tex]\begin{aligned} \sf 3^n &= \sf 54 \\ n &= \sf log_3(54) \\&= \sf log_3(27 \times 2) \\&= \sf log_3(27) + log_3(2) \\&= \sf log_3(3^3) + log_3(2) \\&= \sf 3 + log_3(2) \end{aligned}[/tex]
[tex]\begin{aligned} \sf 9^{n - 2} &= \sf 9^{3 + log_3(2)-2} \\&= \sf 9^3 \times 9^{log_3(2)} \times 9^{-2} \\&= \sf 9^3 \times (3^2)^{log_3(2)} \times 9^{-2} \\&= \sf 9^3 \times (3)^{2log_3(2)} \times 9^{-2} \\&= \sf 9^3 \times (3)^{log_3(2^2)} \times 9^{-2} \\&= \sf 9^3 \times 2^2 \times 9^{-2} \\&= 9^{3-2} \times 2^2 \\&=\sf 9 \times 4 \\&= \boxed{\bold{\underline{ \sf36}}} \end{aligned}[/tex]
[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at | 02 - 07 - 2023}}[/tex]
Verified answer
Jawab:
Cukup ingat konsep eksponen ini :
[tex]1. a^{m-n} = \frac{a^{m} }{a^{n} } \\2. a^{mn} = (a^{m}) ^{n} = (a^{n}) ^{m}[/tex]