Roboguru

Misalkan  dan  untuk semua nilai  dalam daerah asa...

Misalkan begin mathsize 14px style log presuperscript straight x squared minus 4 straight x plus 4 end presuperscript space left parenthesis straight x plus 2 right parenthesis equals straight a end style dan begin mathsize 14px style log presuperscript straight x squared plus 4 straight x plus 4 end presuperscript space left parenthesis straight x minus 2 right parenthesis equals straight b end style untuk semua nilai begin mathsize 14px style straight x end style dalam daerah asal, maka nilai dari begin mathsize 14px style a b end style adalah ....

Jawaban:

Dengan menerapkan sifat-sifat logaritma:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight a. straight b end cell equals cell open square brackets log presuperscript straight x squared minus 4 straight x plus 4 end presuperscript space left parenthesis straight x plus 2 right parenthesis close square brackets open square brackets log presuperscript straight x squared plus 4 straight x plus 4 end presuperscript space left parenthesis straight x minus 2 right parenthesis close square brackets end cell row blank equals cell left square bracket log presuperscript left parenthesis straight x minus 2 right parenthesis squared end presuperscript space left parenthesis straight x plus 2 right parenthesis right square bracket open square brackets log presuperscript left parenthesis straight x plus 2 right parenthesis squared end presuperscript space left parenthesis straight x minus 2 right parenthesis close square brackets end cell row blank equals cell left square bracket 1 half left curly bracket log presuperscript left parenthesis straight x minus 2 right parenthesis end presuperscript space left parenthesis straight x plus 2 right parenthesis right curly bracket right square bracket left square bracket 1 half left curly bracket log presuperscript left parenthesis straight x plus 2 right parenthesis end presuperscript space left parenthesis straight x minus 2 right parenthesis right curly bracket right square bracket end cell row blank equals cell 1 fourth open square brackets left curly bracket log presuperscript left parenthesis straight x minus 2 right parenthesis end presuperscript space left parenthesis straight x plus 2 right parenthesis right curly bracket left curly bracket log presuperscript left parenthesis straight x plus 2 right parenthesis end presuperscript space left parenthesis straight x minus 2 right parenthesis right curly bracket close square brackets end cell row blank equals cell 1 fourth left parenthesis 1 right parenthesis end cell row blank equals cell 1 fourth end cell end table end style 

Jadi, Nilai dari  a.b adalah begin mathsize 14px style 1 fourth end style.

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