Ln(x + 2) = ln(12) − ln(x + 3)
1 answer:
Answer:
x = 1 , -6
Step-by-step explanation:
given,
ln (x + 2) = ln (12) − ln (x + 3)
using identity of logarithm
ln (ab) = ln (a) + ln (b)
ln (a) - ln(b) = ln (a/b)
now
ln (x + 2) = ln (12) − ln (x + 3)
ln (x + 2) =
on comparing
(x+2)(x+3) = 12
x² + 5 x + 6 = 12
x² + 5 x - 6 = 0
x² + 6 x - x - 6 = 0
x(x + 6) -1 (x+ 6) = 0
(x - 1)(x + 6) = 0
x = 1 , -6
Hence, the value of x comes out to be x = 1 , -6
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Answer:
y = (x + 9)² + 9
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
given a parabola in standard form : ax² + bx + c : a ≠ 0
the the x-coordinate of the vertex is
= -
y = x² + 18x + 90 is in standard form
with a = 1, b= 18 and c = 90
= -
= - 9
to find the corresponding y-coordinate substitute x = - 9 into the equation
y = (- 9)² + 18(- 9) + 90 = 81 - 162 + 90 = 9
⇒ y = (x + 9)² + 9 ← in vertex form