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5. Bilangan begin mathsize 14px style log space left parenthesis straight a cubed straight b right parenthesis end styleError converting from MathML to accessible text.Error converting from MathML to accessible text. merupakan tiga suku pertama barisan aritmatika. Jika suku ke-29 barisan tersebut adalah size 14px log size 14px space size 14px left parenthesis size 14px b to the power of size 14px 2 size 14px p end exponent size 14px right parenthesis, Maka nilai dari begin mathsize 14px style 3 straight p equals space.... end style

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style 3 straight p equals 3 left parenthesis 58 right parenthesis equals 174 end style.

Pembahasan

Dengan menerapkan konsep barisan aritmatika.

begin mathsize 14px style straight U subscript 1 equals end stylebegin mathsize 14px style log space left parenthesis straight a cubed straight b right parenthesis end style

Error converting from MathML to accessible text.Error converting from MathML to accessible text.

Error converting from MathML to accessible text.Error converting from MathML to accessible text.

begin mathsize 14px style straight U subscript 29 equals end stylesize 14px log size 14px space size 14px left parenthesis size 14px b to the power of size 14px 2 size 14px p end exponent size 14px right parenthesis 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell Beda  ( straight b )= straight U subscript 3 minus straight U subscript 2 end cell equals cell straight U subscript 2 minus straight U subscript 1 end cell row blank left right double arrow cell straight U subscript 3 minus 2 straight U subscript 2 plus straight U subscript 1 equals 0 end cell row cell log left parenthesis straight a to the power of 5 straight b to the power of 7 right parenthesis minus 2 log left parenthesis straight a squared straight b to the power of 6 right parenthesis plus log left parenthesis straight a cubed straight b right parenthesis end cell equals 0 row cell log left parenthesis straight a to the power of 5 straight b to the power of 7 right parenthesis minus log left parenthesis straight a squared straight b to the power of 6 right parenthesis squared plus log left parenthesis straight a cubed straight b right parenthesis end cell equals 0 row cell log left parenthesis straight a to the power of 5 straight b to the power of 7 right parenthesis minus log left parenthesis straight a to the power of 4 straight b to the power of 12 right parenthesis plus log left parenthesis straight a cubed straight b right parenthesis end cell equals 0 row cell log space fraction numerator left parenthesis straight a to the power of 5 straight b to the power of 7 right parenthesis left parenthesis straight a cubed straight b right parenthesis over denominator left parenthesis straight a to the power of 4 straight b to the power of 12 right parenthesis end fraction end cell equals 0 row cell log space fraction numerator left parenthesis straight a to the power of 8 straight b to the power of 8 right parenthesis over denominator left parenthesis straight a to the power of 4 straight b to the power of 12 right parenthesis end fraction end cell equals 0 row cell log space fraction numerator left parenthesis straight a to the power of 4 right parenthesis over denominator left parenthesis straight b to the power of 4 right parenthesis end fraction end cell equals 0 row cell log space straight a to the power of 4 minus log space straight b to the power of 4 end cell equals 0 row cell log space straight a to the power of 4 end cell equals cell log space straight b to the power of 4 end cell row cell straight a to the power of 4 end cell equals cell straight b to the power of 4 end cell row straight a equals straight b end table end style 

Jadi:

Error converting from MathML to accessible text. 

Error converting from MathML to accessible text. 

Error converting from MathML to accessible text. 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell beda space left parenthesis straight b right parenthesis end cell equals cell 8 log space straight a minus 4 log space 2 end cell row blank equals cell 4 log space straight a end cell end table end style

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 29 end cell equals cell straight U subscript 1 plus left parenthesis 29 minus 1 right parenthesis straight b end cell row cell log space left parenthesis straight a to the power of 2 straight p end exponent right parenthesis end cell equals cell 4 space log space straight a space plus 28 left parenthesis 4 log space straight a right parenthesis end cell row cell log space left parenthesis straight a to the power of 2 straight p end exponent right parenthesis end cell equals cell 4 space log space straight a space plus left parenthesis 112 log space straight a right parenthesis end cell row cell log space left parenthesis straight a to the power of 2 straight p end exponent right parenthesis end cell equals cell 116 log space straight a end cell row cell log space left parenthesis straight a to the power of 2 straight p end exponent right parenthesis end cell equals cell log space straight a to the power of 116 end cell row cell 2 straight p end cell equals 116 row straight p equals 58 end table end style 

Dengan demikian, begin mathsize 14px style 3 straight p equals 3 left parenthesis 58 right parenthesis equals 174 end style.

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