Question

Kuis ₍₁₀₂₎ :
² log ( a + 15 ) = ½ ( 6 + ² log a )

a = { ..................... , ...................... }

Answer 1

Verified answer

²log(a + 15) = ½(6 + ²log a)

²log(a + 15) = 3 + ½ ²log a

²log(a + 15) = ²log2³ + ²log a^(½)

²log(a + 15) = ²log8 + ²log√a

a + 15 = 8√a

(a + 15)² = (8√a)²

a² + 30a + 225 = 64a

a² + 30a - 64a + 225 = 0

a² - 34a + 225 = 0

[tex]a=\frac{-(-34)\pm \sqrt{-34^{2}-4(1)(225) } }{2(1)}\\\\a=\frac{34\pm \sqrt{34^{2}-900 } }{2}\\ \\a=\frac{34\pm \sqrt{1156-900} }{2}\\ \\a=\frac{34\pm \sqrt{256} }{2}\\\\a=\frac{34\pm 16 }{2}[/tex]

a₁ = (34 + 16)/2 = 50/2 = 25

a₂ = (34 - 16)/2 = 18/2 = 9

Jadi, a = {25, 9}.