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Jika 3 ⋅ 8 1 4 9 n ⋅ 3 5 ⋅ 2 7 3 = 27 ,maka nilai n adalah ....

Jika $\frac{9 ^{n} \cdot 3 ^{5} \cdot 2 7 ^{3}}{3 \cdot 8 1 ^{4}} = 27$ , maka nilai n adalah ....

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N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 9 to the power of n times 3 to the power of 5 times 27 cubed over denominator 3 times 81 to the power of 4 end fraction end cell equals 27 row cell fraction numerator open parentheses 3 squared close parentheses to the power of n times 3 to the power of 5 times open parentheses 3 cubed close parentheses cubed over denominator 3 times open parentheses 3 to the power of 4 close parentheses to the power of 4 end fraction end cell equals cell 3 cubed end cell row cell fraction numerator 3 to the power of 2 n end exponent times 3 to the power of 5 times 3 to the power of 9 over denominator 3 times 3 to the power of 16 end fraction end cell equals cell 3 cubed end cell row cell 3 to the power of 2 n plus 5 plus 9 end exponent over 3 to the power of 1 plus 16 end exponent end cell equals cell 3 cubed end cell row cell 3 to the power of 2 n plus 14 end exponent over 3 to the power of 17 end cell equals cell 3 cubed end cell row cell 3 to the power of 2 n plus 14 minus 17 end exponent end cell equals cell 3 cubed end cell row cell 3 to the power of 2 n minus 3 end exponent end cell equals cell 3 cubed end cell row cell 2 n minus 3 end cell equals 3 row cell 2 n end cell equals 6 row n equals cell box enclose 3 end cell end table end style$