Roboguru

Nilai  yang memenuhi  adalah

Pertanyaan

Nilai begin mathsize 14px style x end style yang memenuhi begin mathsize 14px style left parenthesis 4 right parenthesis space l presuperscript 4 o g space x minus left parenthesis 5 right parenthesis space left parenthesis 2 right parenthesis space log presuperscript 2 space x minus 6 equals 0 end style adalah begin mathsize 14px style... end style 

  1. begin mathsize 14px style... end style 

  2. begin mathsize 14px style... end style 

Pembahasan Soal:

Sifat Logaritma :

begin mathsize 14px style ring operator space log presuperscript a to the power of n end presuperscript space b to the power of m equals m over n space space presuperscript a log space b comma space n not equal to 0 ring operator space log presuperscript a space a space equals 1 end style 

Sifat eksponen :

 begin mathsize 14px style ring operator space open parentheses a over b close parentheses to the power of negative n end exponent equals open parentheses b over a close parentheses to the power of n ring operator space a to the power of m over n end exponent equals n-th root of a to the power of m end root ring operator space a to the power of m over a to the power of n equals a to the power of m minus n end exponent end style 

Maka :

begin mathsize 14px style left parenthesis 4 right parenthesis space log presuperscript 4 space x minus left parenthesis 5 right parenthesis space left parenthesis 2 right parenthesis space log presuperscript 2 space x minus 6 equals 0 left parenthesis 4 right parenthesis space log presuperscript 2 squared end presuperscript space x minus left parenthesis 5 right parenthesis space left parenthesis 2 right parenthesis space log presuperscript 2 space x minus 6 equals 0 left parenthesis 4 right parenthesis space open parentheses 1 half close parentheses space log presuperscript 2 space x minus left parenthesis 5 right parenthesis space left parenthesis 2 right parenthesis space log presuperscript 2 space x minus 6 equals 0 left parenthesis 2 right parenthesis space log presuperscript 2 space x minus left parenthesis 5 right parenthesis space left parenthesis 2 right parenthesis space log presuperscript 2 space x minus 6 equals 0  end style  

misal :

begin mathsize 14px style log presuperscript 2 space x space equals a end style 

maka :

begin mathsize 14px style left parenthesis 2 right parenthesis space log presuperscript 2 space x minus left parenthesis 5 right parenthesis space left parenthesis 2 right parenthesis space log presuperscript 2 space x minus 6 equals 0 2 a minus 10 a minus 6 equals 0 minus 8 a minus 6 equals 0 minus 8 a equals 6 a equals negative 6 over 8 a equals negative 3 over 4 end style

Karena begin mathsize 14px style log presuperscript 2 space x space equals a end style, maka :

begin mathsize 14px style x log presuperscript 2 space x equals a log presuperscript 2 space x equals negative 3 over 4 log presuperscript 2 space x equals log presuperscript 2 space open parentheses 2 close parentheses to the power of open parentheses negative 3 over 4 close parentheses end exponent up diagonal strike log presuperscript 2 end strike space x equals up diagonal strike log presuperscript 2 end strike space open parentheses 2 close parentheses to the power of open parentheses negative 3 over 4 close parentheses end exponent space space space space space space space x equals 2 to the power of open parentheses negative 3 over 4 close parentheses end exponent space space space space space space x equals open parentheses 1 half close parentheses to the power of open parentheses 3 over 4 close parentheses end exponent space space space space space space x equals 1 over 2 to the power of open parentheses begin display style 3 over 4 end style close parentheses end exponent space space space space space space x equals fraction numerator 1 over denominator fourth root of 2 cubed end root end fraction space space space space space space x equals fraction numerator 1 over denominator fourth root of 2 cubed end root end fraction cross times fraction numerator fourth root of 2 cubed end root over denominator fourth root of 2 cubed end root end fraction space space space space space space x equals fraction numerator fourth root of 2 cubed end root over denominator square root of 2 cubed end root end fraction space space space space space x equals fraction numerator fourth root of 2 cubed end root over denominator 2 space square root of 2 end fraction space space space space space space x equals fraction numerator 2 to the power of begin display style 3 over 4 end style end exponent over denominator left parenthesis 2 right parenthesis space 2 to the power of begin display style 1 half end style end exponent end fraction space space space space space space x equals 2 to the power of open parentheses begin display style 3 over 4 end style minus begin display style 1 half end style close parentheses end exponent over 2 space space space space space space x equals 2 to the power of begin display style 1 fourth end style end exponent over 2 space space space space space space x equals fraction numerator fourth root of 2 over denominator 2 end fraction end style  

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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