Tentukan nilai x yang memenuhi persamaan
[tex]\large ^x\log 2~^{\frac{x}{16}}\log 2=^{\frac{x}{64}}\log 2[/tex]
[tex]\large ^x\log 2~^{\frac{x}{16}}\log 2=^{\frac{x}{64}}\log 2[/tex]
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Verified answer
LOGARITMA
log (a/b) = log a - log b
soal
kedua ruas bagi dengan (log 2)
1/log x × log 2 /log (x/16) = 1/log (x/64)
log 2 × log (x/64) = log x × log (x/16)
log 2 (log x - 6 log 2) = log x (log x - 4 log 2)
log² x - 4 log 2 log x - log 2 log x + 6 log² 2 = 0
log² x - 5 log 2 log x + 6 log² x = 0
(log x - 2 log 2)(log x - 3 log 2) = 0
log x - log 2² = 0
x = 2²
x = 4
log x - log 2³ = 0
x = 2³
x = 8
x = {4 , 8}