F(x) = log 2(x + 7) and g(x) = log 2(3x + 5).
(a) solve f(x) = 4 what point is on the graph of f?
(b) solve g(x) = 3. what point is on the graph of g?
(c) solve f(x) = g(x). do the graphs off and g intersect? if so, where?
(d) solve (f + g)(x) = 9
(e) solve (f-9)(x) = 3

(a) x = 9, (9,4)

(b) x = 1, (1,3)

(c) x = 1 and the graph of f(x) and g(x) intersects at point (1,3)

(d) or x = 9

(e)

Step-by-step explanation:

We are given that ....... (1),and  

........ (2)

Now,  

(a) We have to solve f(x) = 4

⇒

Converting logarithm to exponent form, we get,

⇒ x = 9 (Answer)

Now, the point on the graph of f(x) will be (9,4) (Answer)

(b) We have to solve g(x) = 3

⇒

Converting logarithm to exponent form, we get,

⇒ x = 1 (Answer)

Now, the point on the graph of g(x) will be (1,3) (Answer)

(c) We have to solve f(x) = g(x)

⇒

Now comparing both sides we can write

x + 7 = 3x + 5  

⇒ 2x = 2  

⇒ x = 1 (Answer)

Now, at x = 1,  

So, the graph of f(x) and g(x) intersects at point (1,3) (Answer)

(d) We have to solve (f + g)(x) = 9

⇒

⇒  

⇒

⇒ 3x² + 26x - 477 = 0

⇒ (3x + 53)(3x - 27) = 0

Hence, or x = 9 (Answer)

(e) We have to solve (f - g)(x) = 3

⇒

⇒

⇒

⇒ x + 7 = 24x + 40

⇒ 23x = - 33

⇒ (Answer)

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

51

step-by-step explanation:

73-22=51 the   mass number minus the amount of protons gives you the amount of neutrons