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Diberi , hitung nilai !

Pertanyaan

Diberi 3 to the power of 2 y minus 1 end exponent equals open parentheses 9 close parentheses open parentheses 27 close parentheses to the power of y minus 2 end exponent, hitung nilai y

Pembahasan Soal:

3 to the power of 2 y minus 1 end exponent equals open parentheses 9 close parentheses open parentheses 27 close parentheses to the power of y minus 2 end exponent 3 to the power of 2 y minus 1 end exponent equals 3 squared times open parentheses 3 cubed close parentheses to the power of y minus 2 end exponent 3 to the power of 2 y minus 1 end exponent equals 3 squared times 3 to the power of 3 y minus 6 end exponent 3 to the power of 2 y minus 1 end exponent equals 3 to the power of 2 plus 3 y minus 6 end exponent 3 to the power of 2 y minus 1 end exponent equals 3 to the power of 3 y minus 4 end exponent

karena bilangan pokoknya sudah sama maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 y minus 1 end cell equals cell 3 y minus 4 end cell row cell 4 minus 1 end cell equals cell 3 y minus 2 y end cell row 3 equals y end table 

Jadi, nilai y equals 3

 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Roy

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 05 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika , nilai dari

Pembahasan Soal:

Dengan menerapkan sifat bilangan berpangkat, maka dapat dilakukan perhitungan seperti di bawah ini

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator begin mathsize 14px style left parenthesis 3 p squared right parenthesis squared plus left parenthesis 4 p squared right parenthesis squared end style over denominator begin mathsize 14px style left parenthesis 3 p right parenthesis squared minus left parenthesis 2 p right parenthesis squared end style end fraction end cell size 14px equals size 14px 80 row cell fraction numerator begin mathsize 14px style 9 p to the power of 4 plus 16 p to the power of 4 end style over denominator begin mathsize 14px style 9 p squared minus 4 p squared end style end fraction end cell size 14px equals size 14px 80 row cell fraction numerator begin mathsize 14px style 25 p to the power of 4 end style over denominator begin mathsize 14px style 5 p squared end style end fraction end cell size 14px equals size 14px 80 row cell size 14px 5 size 14px p to the power of size 14px 2 end cell size 14px equals size 14px 80 row cell size 14px p to the power of size 14px 2 end cell size 14px equals size 14px 16 end table

Jadi, jawaban yang tepat adalah B.

0

Roboguru

Jika , maka nilai

Pembahasan Soal:

Ingat :

a c plus b c equals left parenthesis a plus b right parenthesis c
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
Jikaspace a to the power of f italic left parenthesis x italic right parenthesis end exponent italic equals a to the power of p comma makaspace f italic left parenthesis x italic right parenthesis italic equals p dengan a italic greater than italic 0 italic spacedan space a italic not equal to italic 1

maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 13 left parenthesis 5 to the power of 4 right parenthesis plus 12 left parenthesis 5 to the power of 4 right parenthesis end cell equals cell 5 to the power of p plus q end exponent end cell row cell left parenthesis 13 plus 12 right parenthesis left parenthesis 5 to the power of 4 right parenthesis end cell equals cell 5 to the power of p plus q end exponent end cell row cell space space space space space space space space 25 cross times 5 to the power of 4 end cell equals cell 5 to the power of p plus q end exponent end cell row cell space space space space space space space space 5 squared cross times 5 to the power of 4 end cell equals cell 5 to the power of p plus q end exponent end cell row cell 5 to the power of 2 plus 4 end exponent end cell equals cell 5 to the power of p plus q end exponent end cell row cell space space space space space space space space space space space space space space space space 5 to the power of 6 end cell equals cell 5 to the power of p plus q end exponent end cell row cell space space space space space space space space space space space space space space space space space space 6 end cell equals cell space p plus q end cell end table

Jadi, jawaban yang tepat adalah B.

3

Roboguru

Jika , maka nilai  adalah ....

Pembahasan Soal:

Ingat :

a d plus b d plus c d equals left parenthesis a plus b plus c right parenthesis d

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

Jikaspace a to the power of f italic left parenthesis x italic right parenthesis end exponent italic equals a to the power of p comma makaspace f italic left parenthesis x italic right parenthesis italic equals p dengan a italic greater than italic 0 italic spacedan space a italic not equal to italic 1

maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 cubed plus 3 left parenthesis 2 cubed right parenthesis plus 4 left parenthesis 2 cubed right parenthesis end cell equals cell 2 to the power of n end cell row cell space space space space space space space space left parenthesis 1 plus 3 plus 4 right parenthesis 2 cubed end cell equals cell 2 to the power of n end cell row cell space space space space space space space space space space space space space space space space space space space left parenthesis 8 right parenthesis 2 cubed space end cell equals cell 2 to the power of n end cell row cell space space space space space space space space space space space space space space space space 2 cubed cross times 2 cubed space end cell equals cell 2 to the power of n end cell row cell 2 to the power of 3 plus 3 end exponent end cell equals cell 2 to the power of n end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space 2 to the power of 6 end cell equals 2 row cell space space space space space space space space space space space space space space space space space space space space space space space space space space n end cell equals 6 end table

Jadi, jawaban yang tepat adalah A.

3

Roboguru

Bentuk sederhana dari  adalah ....

Pembahasan Soal:

Ingat:

begin mathsize 14px style a to the power of m colon a to the power of n equals a to the power of m minus n end exponent end style

undefined

undefined

maka

table attributes columnalign right center left columnspacing 0px end attributes row cell p to the power of 3 over 2 end exponent cross times p to the power of negative 2 over 5 end exponent colon p to the power of negative 1 7 over 30 end exponent end cell equals cell p to the power of 3 over 2 end exponent cross times p to the power of negative 2 over 5 end exponent colon p to the power of negative 37 over 30 end exponent end cell row blank equals cell p to the power of 3 over 2 plus open parentheses negative 2 over 5 close parentheses minus open parentheses negative 37 over 30 close parentheses end exponent end cell row blank equals cell p to the power of 3 over 2 minus 2 over 5 plus 37 over 30 end exponent end cell row blank equals cell p to the power of fraction numerator 45 minus 12 plus 37 over denominator 30 end fraction end exponent end cell row blank equals cell p to the power of 70 over 30 end exponent end cell row blank equals cell p to the power of 7 over 3 end exponent end cell row blank equals cell cube root of p to the power of 7 end root end cell row blank equals cell cube root of p to the power of 6 p end root end cell row blank blank blank end table

Jadi, pilihan jawaban yang tepat adalah E.

1

Roboguru

Himpunan penyelesaian dari persamaan di bawah ini adalah...

Pembahasan Soal:

Ingat :

open parentheses straight a to the power of straight m close parentheses to the power of straight n equals straight a to the power of mn straight a to the power of straight m plus straight n end exponent equals straight a to the power of straight m times straight a to the power of straight n

Maka,

4 to the power of x minus 3 times 2 to the power of x plus 1 end exponent plus 8 equals 0 open parentheses 2 squared close parentheses to the power of x minus 3 times 2 to the power of x times 2 plus 8 minus 0 open parentheses 2 to the power of x close parentheses squared minus 6 times 2 to the power of x plus 8 equals 0

Misalkan 2 to the power of x equals p, maka

straight p squared minus 6 straight p plus 8 equals 0 left parenthesis straight p minus 2 right parenthesis left parenthesis straight p minus 4 right parenthesis equals 0 straight p equals 2 comma space straight p equals 4 2 to the power of straight x equals 2 rightwards arrow straight x equals 1 2 to the power of straight x equals 4 rightwards arrow straight x equals 2

Jadi, himpunan penyelesaian persamaan tersebut adalah open curly brackets 1 comma space 2 close curly brackets.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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