Roboguru

Jika  maka ...

Pertanyaan

Jika log presuperscript x space 81 equals negative 4 maka x equals...

  1. 3

  2. 2

  3. 1

  4. 1 half

  5. 1 third

Pembahasan Soal:

Diketahui:

log presuperscript x space 81 equals negative 4

Ditanya:

Nilai x

Fungsi logaritma merupakan fungsi invers dari fungsi eksponen. Jika fungsi logaritma dinyatakan dengan y equals a to the power of x dengan a greater than 0 dan a not equal to 1, maka fungsi inversnya adalah y equals log presuperscript a space x dengan a greater than 0a not equal to 1 dan x greater than 0.

Perlu diingat bahwa:

log presuperscript a space a to the power of b equals b space open parentheses a to the power of b close parentheses to the power of c equals a to the power of b times c end exponent 1 over a to the power of b equals a to the power of negative b end exponent

Perhatikan perhitungan berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell log presuperscript x space 81 end cell equals cell negative 4 end cell row cell x to the power of negative 4 end exponent end cell equals 81 row cell x to the power of negative 4 end exponent end cell equals cell 81 to the power of 1 end cell row cell x to the power of negative 4 end exponent end cell equals cell open parentheses 81 to the power of negative 1 end exponent close parentheses to the power of negative 1 end exponent end cell row cell x to the power of negative 4 end exponent end cell equals cell open parentheses 1 over 81 close parentheses to the power of negative 1 end exponent end cell row cell x to the power of negative 4 end exponent end cell equals cell open parentheses 1 over 3 to the power of 4 close parentheses to the power of negative 1 end exponent end cell row cell x to the power of negative 4 end exponent end cell equals cell open parentheses open parentheses 1 third close parentheses to the power of 4 close parentheses to the power of negative 1 end exponent end cell row cell x to the power of negative 4 end exponent end cell equals cell open parentheses 1 third close parentheses to the power of negative 4 end exponent end cell row x equals cell 1 third end cell end table

Sehingga, nilai x yang tepat adalah 1 third.

Jadi, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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