Nyatakan 31​alog x−5 alog y+alog z sebagai suatu logaritma tunggal.

Pertanyaan

Nyatakan begin mathsize 14px style 1 third log presuperscript a space x minus 5 space log presuperscript a space y plus log presuperscript a space z end style sebagai suatu logaritma tunggal.

F. Isyrofinnisak

Master Teacher

Jawaban terverifikasi

Jawaban

logaritma tunggal dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third log presuperscript a space x minus 5 space log presuperscript a space y plus log presuperscript a space z end cell end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell log presuperscript a space open parentheses fraction numerator cube root of x times z over denominator y to the power of 5 end fraction close parentheses end cell end table.

Pembahasan

Ingat kosep :

blank to the power of a log space b to the power of m equals m times to the power of a log space b to the power of a log space left parenthesis b c right parenthesis equals to the power of a log space b space plus to the power of a log space c space to the power of a log space open parentheses b over c close parentheses equals to the power of a log space b space minus space to the power of a log space c 

Dari konsep logaritma, maka soal diatas dapat diselesaikan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 third log presuperscript a space x minus 5 space log presuperscript a space y plus log presuperscript a space z end cell equals cell log presuperscript a space x to the power of 1 third end exponent minus log presuperscript a space y to the power of 5 plus log presuperscript a space z end cell row blank equals cell log presuperscript a space open parentheses fraction numerator cube root of x times z over denominator y to the power of 5 end fraction close parentheses end cell end table   

Dengan demikian logaritma tunggal dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third log presuperscript a space x minus 5 space log presuperscript a space y plus log presuperscript a space z end cell end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell log presuperscript a space open parentheses fraction numerator cube root of x times z over denominator y to the power of 5 end fraction close parentheses end cell end table.

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