Solve each equation. Round your answers to the nearest ten-thousandth. Please show your work. Part 4A

22.

     log3(4) + log3(5x^2 + 1) = 2

<=> log3(4 x (5x^2 + 1)) = log3(9)

<=> 20x^2 + 4 = 9

<=> 20x^2 = 5

<=> x^2 = 1/4

<=> x = +/- (1/2)

23.

      log8(4x^2 + 1) - log8(2) = log8(5)

<=> log8((4x^2 + 1)/2) = log8(5)

<=> 2x^2 + 1/2 = 5

<=> 2x^2 = 9/2

<=> x^2 = 9/4

<=> x = +- (3/2)

24.

      log8(4x^2 - 9) - log8(5) = 1

<=> log8((4x^2 - 9)/5) = log8(8)

<=> (4x^2 - 9)/5 = 8

<=> 4x^2 - 9 = 40

<=> 4x^2 = 49

<=> x^2 = 49/4

<=> x = +/- (7/2)

Hope this helps!

:)

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation:

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)