Log (x2 - 1) - log (2x + 2) = 0

x=3

Step-by-step explanation:

log (x^2 - 1) - log (2x + 2) = 0

Add log (2x + 2) to each side

log (x^2 - 1) = log (2x + 2)

Since the logs with the same base are equal the x^2 -1 must equal 2x+2

x^2 -1 = 2x+2

Subtract 2x+2 from each side

x^2 -1 -2x-2 = 2x+2 -2x-2

x^2 -2x-3 = 0

Factor

What number multiplies to -3 and adds to -2

-3 *1 =-3

-3+1 =-2

(x-3) (x+1) =0

Using the zero product property

x-3 =0   x+1 =0

x=3  x=-1

Check to see if solutions are valid

x = -1

log ((-1)^2 - 1) - log (2*-1 + 2) = 0

log(0) - log 0 = 0

Log 0 is undefined  x =-1 not a valid solution

x = 3

log ((3)^2 - 1) - log (2*3 + 2) = 0

log(8) - log 8 = 0

valid

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm