Pertanyaan

Jika 2 a + 2 ⋅ 2 lo g a + 2 a − 2 ⋅ 2 lo g a = 10 ⋅ 2 a − 3 , maka a = ....

Jika $2^{a + 2} \cdot^{2} lo g a + 2^{a - 2} \cdot^{2} lo g a = 10 \cdot 2^{a - 3}$ , maka $a = ....$

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Dengan menggunakan sifat pangkat dan logaritma, diperoleh: Jika nilai dibulatkan, maka diperoleh . Jadi, jawaban yang tepat adalah A.

Dengan menggunakan sifat pangkat dan logaritma, diperoleh:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of a plus 2 end exponent times log presuperscript 2 space a plus 2 to the power of a minus 2 end exponent times log presuperscript 2 space a end cell equals cell 10 times 2 to the power of a minus 3 end exponent end cell row cell up diagonal strike 2 to the power of a end strike times 2 squared times open parentheses scriptbase log space a end scriptbase presuperscript 2 close parentheses plus up diagonal strike 2 to the power of a end strike times 2 to the power of negative 2 end exponent times open parentheses scriptbase log space a end scriptbase presuperscript 2 close parentheses end cell equals cell 10 times up diagonal strike 2 to the power of a end strike times 2 to the power of negative 3 end exponent end cell row cell 4 times open parentheses scriptbase log space a end scriptbase presuperscript 2 close parentheses plus 1 fourth open parentheses scriptbase log space a end scriptbase presuperscript 2 close parentheses end cell equals cell 10 times 1 over 8 end cell row cell fraction numerator 16 plus 1 over denominator 4 end fraction open parentheses scriptbase log space a end scriptbase presuperscript 2 close parentheses end cell equals cell 10 over 8 end cell row cell 17 over 4 open parentheses scriptbase log space a end scriptbase presuperscript 2 close parentheses end cell equals cell 10 over 8 end cell row cell scriptbase log space a end scriptbase presuperscript 2 end cell equals cell 10 over 8 times 4 over 17 end cell row cell scriptbase log space a end scriptbase presuperscript 2 end cell equals cell 40 over 136 end cell row cell scriptbase log space a end scriptbase presuperscript 2 end cell equals cell 5 over 17 end cell row a equals cell 2 to the power of 5 over 17 end exponent end cell row a almost equal to cell 1 comma 2261 end cell end table end style$

Jika nilai dibulatkan, maka diperoleh a equals 1 .

Jadi, jawaban yang tepat adalah A.