Solve the equation below for x.
500 = 25e ^ (2x)

x = i π n + log(20)/2 for n element Z

Step-by-step explanation:

Solve for x:

500 = 25 e^(2 x)

500 = 25 e^(2 x) is equivalent to 25 e^(2 x) = 500:

25 e^(2 x) = 500

Divide both sides by 25:

e^(2 x) = 20

Take the natural logarithm of both sides:

2 x = 2 i π n + log(20) for n element Z

Divide both sides by 2:

x = i π n + log(20)/2 for n element Z

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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