nilai x yang memenuhi 5 log (x + 5)+5 log(x-3)-5 log(x+15)=0

5'log (x + 5) + 5'log (x - 3) - 5'log (x + 15) = 0
5'log (x + 5)(x - 3)/(x + 15) = 5'log 1
(x + 5)(x - 3)/(x + 15) = 1
Kalikan silang
(x + 5)(x - 3) = x + 15
x² + 2x - x - 15 - 15 = 0
x² + x - 30 = 0
(x - 5)(x + 6) = 0
x = 5 atau x = -6

syarat numerus : > 0

nilai x yg memenuhi :
x = 5

Bab Logaritma
Matematika SMA Kelas X

⁵log (x + 5) + ⁵log (x - 3) - ⁵log (x + 15) = 0
⁵log ((x + 5) . (x - 3) /(x + 15)) = 0
(x + 5) . (x - 3) / (x + 15) = 5⁰
(x + 5) . (x - 3) = 1 . (x + 15)
x² + 2x - 15 = x + 15
x² + 2x - 15 - x - 15 = 0
x² + x - 30 = 0
(x + 6) (x - 5) = 0
x + 6 = 0
x = -6 (tidak memenuhi karena negatif)

x - 5 = 0
x = 5 (memenuhi karena positif)

HP = { 5 }

pembuktian

⁵log (5 + 5) + ⁵log (5 - 3) - ⁵log (5 + 15) = ⁵log 10 + ⁵log 2 - ⁵log 20
                                                              = ⁵log (10 x 2 : 20)
                                                              = ⁵log 1
                                                              = 0

terbukti