Pertanyaan

Jika , maka nilai 2a + 2b adalah ....

Jika $87 open parentheses 5 to the power of 7 close parentheses plus 38 open parentheses 5 to the power of 7 close parentheses equals 25 to the power of fraction numerator a plus b over denominator 4 end fraction end exponent$ , maka nilai 2a + 2b adalah ....

S. Nur

Master Teacher

Jawaban terverifikasi

Pembahasan

(ingat sistem distribusi perkalian) Karena bilangan pokoknya sama maka :

(ingat sistem distribusi perkalian)

$begin mathsize 16px style open parentheses 87 plus 38 close parentheses open parentheses 5 to the power of 7 close parentheses equals open parentheses 5 squared close parentheses to the power of fraction numerator a plus b over denominator 4 end fraction end exponent 125 cross times 5 to the power of 7 equals 5 to the power of fraction numerator a plus b over denominator 2 end fraction end exponent 5 cubed cross times 5 to the power of 7 equals 5 to the power of fraction numerator a plus b over denominator 2 end fraction end exponent open parentheses ingat space a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent close parentheses 5 to the power of 3 plus 7 end exponent equals 5 to the power of fraction numerator a plus b over denominator 2 end fraction end exponent 5 to the power of 10 equals 5 to the power of fraction numerator a plus b over denominator 2 end fraction end exponent end style$

Karena bilangan pokoknya sama maka :

$fraction numerator a plus b over denominator 2 end fraction equals 10 a plus b equals 10 cross times 2 space a plus b equals 20 Maka space 2 straight a plus 2 straight b equals 2 open parentheses straight a plus straight b close parentheses equals 2 cross times 20 equals 40$