Buktikan kesamaan logaritma berikut b. 2×4log 45−4log 53​−3×4log 5=3×4log 3

Pertanyaan

Buktikan kesamaan logaritma berikut

b. 2 cross times log presuperscript 4 space 45 minus log presuperscript 4 space begin inline style 3 over 5 end style minus 3 cross times log presuperscript 4 space 5 equals 3 cross times log presuperscript 4 space 3   

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

terbukti bahwa 2 cross times log presuperscript 4 space 45 minus log presuperscript 4 space begin inline style 3 over 5 end style minus 3 cross times log presuperscript 4 space 5 equals 3 cross times log presuperscript 4 space 3

Pembahasan

Ingat sifat bentuk logaritma:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript a space b c end cell equals cell log presuperscript a space b plus log presuperscript a space c end cell row cell log presuperscript a space begin inline style b over c end style end cell equals cell log presuperscript a space b minus log presuperscript a space c end cell row cell log presuperscript a space b to the power of m end cell equals cell m log presuperscript a space b end cell end table   

Dengan membuktikan ruas kiri sama dengan ruas kanan maka:

2 cross times log presuperscript 4 space 45 minus log presuperscript 4 space begin inline style 3 over 5 end style minus 3 cross times log presuperscript 4 space 5 equals 2 cross times log presuperscript 4 space open parentheses 9 cross times 5 close parentheses minus open parentheses log presuperscript 4 space 3 minus log presuperscript 4 space 5 close parentheses minus 3 cross times log presuperscript 4 space 5 equals 2 cross times log presuperscript 4 space 9 plus 2 cross times log presuperscript 4 space 5 minus log presuperscript 4 space 3 plus log presuperscript 4 space 5 minus 3 cross times log presuperscript 4 space 5 equals 2 cross times log presuperscript 4 space 3 squared minus log presuperscript 4 space 3 plus 2 cross times log presuperscript 4 space 5 minus 3 cross times log presuperscript 4 space 5 plus log presuperscript 4 space 5 equals 2 cross times 2 space log presuperscript 4 space 3 minus log presuperscript 4 space 3 plus open parentheses 2 minus 3 plus 1 close parentheses cross times log presuperscript 4 space 5 equals 4 cross times space log presuperscript 4 space 3 minus log presuperscript 4 space 3 plus open parentheses 0 close parentheses cross times log presuperscript 4 space 5 equals open parentheses 4 minus 1 close parentheses log presuperscript 4 space 3 plus 0 equals 3 cross times log presuperscript 4 space 3   

Dengan demikian terbukti bahwa 2 cross times log presuperscript 4 space 45 minus log presuperscript 4 space begin inline style 3 over 5 end style minus 3 cross times log presuperscript 4 space 5 equals 3 cross times log presuperscript 4 space 3

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Jika 16log (x−2)−16log (x2−4x+4)1​=−2, tentukan nilai x yang memenuhi persamaan tersebut.

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