Jumlah nilai x yang memenuhi: (3​+1)x+4(23​−1​)x=8 adalah...

Pertanyaan

Jumlah nilai begin mathsize 14px style x end style yang memenuhi:

begin mathsize 14px style open parentheses square root of 3 plus 1 close parentheses to the power of x plus 4 open parentheses fraction numerator square root of 3 minus 1 over denominator 2 end fraction close parentheses to the power of x equals 8 end style

adalah...

  1. begin mathsize 14px style 3 over 2 end style

  2. begin mathsize 14px style 2 end style

  3. begin mathsize 14px style scriptbase log open parentheses square root of 3 plus 1 close parentheses end scriptbase presuperscript 2 end style

  4. begin mathsize 14px style scriptbase log open parentheses 8 close parentheses end scriptbase presuperscript open parentheses square root of 3 plus 1 close parentheses end presuperscript end style

  5. begin mathsize 14px style scriptbase log open parentheses 4 close parentheses end scriptbase presuperscript open parentheses square root of 3 plus 1 close parentheses end presuperscript end style

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Misalkan 

begin mathsize 14px style y equals left parenthesis square root of 3 plus 1 right parenthesis to the power of x end style

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator square root of 3 minus 1 over denominator 2 end fraction close parentheses to the power of x end cell equals cell open parentheses fraction numerator square root of 3 minus 1 over denominator 2 end fraction cross times fraction numerator square root of 3 plus 1 over denominator square root of 3 plus 1 end fraction close parentheses to the power of x end cell row blank equals cell open parentheses fraction numerator 3 minus 1 over denominator 2 open parentheses square root of 3 plus 1 close parentheses end fraction close parentheses to the power of x end cell row blank equals cell open parentheses fraction numerator 2 over denominator 2 open parentheses square root of 3 plus 1 close parentheses end fraction close parentheses to the power of x end cell row blank equals cell 1 over open parentheses square root of 3 plus 1 close parentheses to the power of x end cell row blank equals cell 1 over y end cell end table end style

Sehingga diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis square root of 3 plus 1 right parenthesis to the power of x plus 4 left parenthesis fraction numerator square root of 3 minus 1 over denominator 2 end fraction right parenthesis to the power of x end cell equals 8 row cell y plus 4 1 over y end cell equals 8 row cell y squared plus 4 end cell equals cell 8 y end cell row cell y squared minus 8 y plus 4 end cell equals 0 end table end style

Misalkan begin mathsize 14px style y subscript 1 end style dan begin mathsize 14px style y subscript 2 end style akar-akar persamaan kuadrat Error converting from MathML to accessible text. maka diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell y subscript 1 y subscript 2 end cell equals cell fraction numerator negative open parentheses negative 8 close parentheses over denominator 1 end fraction end cell row cell y subscript 1 y subscript 2 end cell equals 8 row cell open parentheses square root of 3 plus 1 close parentheses to the power of x subscript 1 end exponent open parentheses square root of 3 plus 1 close parentheses to the power of x subscript 2 end exponent end cell equals 8 row cell open parentheses square root of 3 plus 1 close parentheses to the power of x subscript 1 plus x subscript 2 end exponent end cell equals 8 row cell x subscript 1 plus x subscript 2 end cell equals cell scriptbase log open parentheses 8 close parentheses end scriptbase presuperscript open parentheses square root of 3 plus 1 close parentheses end presuperscript end cell end table end style

Dengan demikian jumlah nilai begin mathsize 14px style x end style yang memenuhi begin mathsize 14px style left parenthesis square root of 3 plus 1 right parenthesis to the power of x plus 4 left parenthesis fraction numerator square root of 3 minus 1 over denominator 2 end fraction right parenthesis to the power of x equals 8 end style adalah Error converting from MathML to accessible text..

Oleh karena itu, jawaban yang benar adalah D.

66

4.2 (4 rating)

mewilanda

Ini yang aku cari! Makasih ❤️

Amanda Deby febrina

Makasih ❤️

Adinda Amelia

Jawaban tidak sesuai

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