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Pertanyaan

Jika a dan b adalah bilangan dengan a > 1 dan b > 0 . Jika ab = a b dan b a ​ = a 3 b , maka nilai a = ....

Jika a dan b adalah bilangan dengan > 1 dan > 0. Jika  dan , maka nilai a = ....

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N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa Sehingga Maka

Perhatikan bahwa

begin mathsize 14px style a over b equals a to the power of 3 b end exponent a over b equals open parentheses a to the power of b close parentheses cubed a over b equals open parentheses a b close parentheses cubed a over b equals a cubed b cubed a equals a cubed b cubed b a over a cubed equals b cubed b a to the power of 1 minus 3 end exponent equals b to the power of 3 plus 1 end exponent a to the power of negative 2 end exponent equals b to the power of 4 open parentheses a to the power of negative 2 end exponent close parentheses to the power of negative 1 half end exponent equals open parentheses b to the power of 4 close parentheses to the power of negative 1 half end exponent box enclose a equals b to the power of negative 2 end exponent end enclose end style

Sehingga

begin mathsize 14px style a over b equals a to the power of 3 b end exponent b to the power of negative 2 end exponent over b equals open parentheses b to the power of negative 2 end exponent close parentheses to the power of 3 b end exponent b to the power of negative 2 minus 1 end exponent equals b to the power of negative 6 b end exponent b to the power of negative 3 end exponent equals b to the power of negative 6 b end exponent minus 3 equals negative 6 b b equals box enclose 1 half end enclose end style

Maka

begin mathsize 14px style a equals b to the power of negative 2 end exponent space space equals open parentheses 1 half close parentheses to the power of negative 2 end exponent space space equals open parentheses 2 to the power of negative 1 end exponent close parentheses to the power of negative 2 end exponent space space equals 2 squared space space equals box enclose 4 end style   

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Nilai dari b 3 2 ​ + 3 b − 1 − 2 b 0 a 2 3 ​ + 4 a − 1 − 5 a 0 ​ bila a = 4 dan b = 8 1 ​ adalah ....

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