Matematika

Pertanyaan

Solusi persamaan [tex] 5^{2x+1} = 10^{2x-1} [/tex] adalah...
A.2㏒25
B.2㏒50
C.4㏒25
D.4㏒50
E.5㏒4

Tolong ya... plisss

1 Jawaban

  • log 5^(2x+1) = log 10^(2x-1)
    (2x+1).log 5 = (2x-1).log 10
    (2x+1).log 5 = (2x-1). log 5.2
    (2x+1).log 5 = (2x-1) log 5 + (2x-1) log 2
    2x.log 5 + log 5 = 2x.log 5 -log 5 + 2x.log 2 - log 2.
    log 5 + log 5 = 2x.log 2 - log 2
    log (5×5) = x.log 2^2 - log 2
    log 25 + log 2 = x.log 4
    log (25×2) = x.log 4
    x = log 50/log 4
    x = 4log 50...(D)

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