Matematika

Pertanyaan

diketahui 2log7=p. Nilai 14log98=

2 Jawaban

  • = 2log98 / 2log14 (sifat alogb=nlogb / nloga)
    = 2log(2x49) / 2log(2x7)
    = 2log2 + 2log(7^2) / 2log2+2log7
    = 1 + 2p / 1 + p
  • [tex] 2_{log 7} x 2_{log 2} = p + 1[/tex]
    [tex] 2_{log 14} = p + 1[/tex] -> [tex]14_{log 2} = [tex] \frac{1}{p + 1} [/tex]    A
    [tex] 7_{log 2} + 7_{log 7} = \frac{1}{p} + 1[/tex]
    [tex] 7_{log 14} = \frac{1 + p}{p} [/tex] -> [tex] 14_{log 7 } + 14_{log 7 } = \frac{p + p}{p + 1} [/tex]
    [tex] 14_{log 49} = \frac{2p}{p + 1} [/tex]                                                    B
    A + B =  [tex] 14_{log 2} + 14_{log 49} = \frac{1}{p + 1} + \frac{2p}{p + 1} [/tex]
                 [tex] 14_{log 98} = \frac{2p + 1}{p + 1} [/tex]

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