Pertanyaan

Sederhanakanlah: a. lo g ( x 8 − y 8 ) − lo g ( x 2 + y 2 )

Sederhanakanlah:

a. $lo g (x^{8} - y^{8}) - lo g (x^{2} + y^{2})$

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R. Hajrianti

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

bentuk sederhananya adalah .

bentuk sederhananya adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank log end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x to the power of 6 minus x to the power of 4 y squared plus y to the power of 4 x squared minus y to the power of 6 close parentheses end cell end table

Pembahasan

Ingat kembali sifat bentuk logaritma berikut ini. Dengan sifat bentuk logaritma di atas, didapat perhitungan berikut ini. Jadi, bentuk sederhananya adalah .

Ingat kembali sifat bentuk logaritma berikut ini.

log presuperscript a space open parentheses b over c close parentheses equals log presuperscript a space b minus log presuperscript a space c

Dengan sifat bentuk logaritma di atas, didapat perhitungan berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell log space open parentheses x to the power of 8 minus y to the power of 8 close parentheses minus log space open parentheses x squared plus y squared close parentheses end cell row blank equals cell log space fraction numerator open parentheses x to the power of 8 minus y to the power of 8 close parentheses over denominator open parentheses x squared plus y squared close parentheses end fraction end cell row blank equals cell log space fraction numerator open parentheses x to the power of 4 plus y to the power of 4 close parentheses open parentheses x to the power of 4 minus y to the power of 4 close parentheses over denominator open parentheses x squared plus y squared close parentheses end fraction end cell row blank equals cell log space fraction numerator open parentheses x to the power of 4 plus y to the power of 4 close parentheses up diagonal strike open parentheses x squared plus y squared close parentheses end strike open parentheses x squared minus y squared close parentheses over denominator up diagonal strike open parentheses x squared plus y squared close parentheses end strike end fraction end cell row blank equals cell log space open parentheses x to the power of 4 plus y to the power of 4 close parentheses open parentheses x squared minus y squared close parentheses end cell row blank equals cell log space open parentheses x to the power of 6 minus x to the power of 4 y squared plus y to the power of 4 x squared minus y to the power of 6 close parentheses end cell end table$

Jadi, bentuk sederhananya adalah .