Answer:
The solution is x = e⁶
Step-by-step explanation:
Hi there!
First, let´s write the equation
ln(x⁶) = 36
Apply logarithm property: ln(xᵃ) = a ln(x)
6 ln(x) = 36
Divide both sides of the equation by 6
ln(x) = 6
Apply e to both sides
e^(ln(x)) = e⁶
x = e⁶
The solution is x = e⁶
Let´s prove why e^(ln(x)) = x
Let´s consider this function:
y = e^(ln(x))
Apply ln to both sides of the equation
ln(y) = ln(e^(ln(x)))
Apply logarithm property: ln(xᵃ) = a ln(x)
ln(y) = ln(x) · ln(e) (ln(e) = 1)
ln(y) = ln(x)
Apply logarithm equality rule: if ln(a) = ln(b) then, a = b
y = x
Since y = e^(ln(x)), then x =e^(ln(x))
Have a nice day!
Answer:
what do I want like from it like
Answer: option D is the correct answer.
Step-by-step explanation:
The given figure is a kite. In a kite, the diagonal are perpendicular. It means that the diagonals meet at 90 degrees. Therefore,
Angle 1 = 90 degrees
Angle 3 = 90 degrees
Also, the sum of the angles in a triangle is 180 degrees.
Let x represent the third angle in the right angle triangle containing angle 1 and 50 degrees. It means that
50 + 90 + x = 180
140 + x = 180
x = 180 - 140 = 40 degrees
The pair of opposite sides and opposite angles are congruent. It means that
angle 2 = Angle x
angle 2 = 40 degrees
X=12.5
If the perimeter is 90
90=3x+3x+15
Combine like terms
90=6x+15
Subtracts 15 from both sides
75=6x
Divide by six to get x by itself
12.5=x
Does this help?
Answer:
12 ft
Step-by-step explanation:
we know the areas of the 2 top squares.
the area of a square is simply the square of its side length.
=>
81 ft² means side length is 9 ft.
225 ft² means side length is 15 ft.
these are also 2 of the sides of the right triangle.
the third side we get by using Pythagoras :
c² = a² + b²
with c being the side opposite of the 90 degree angle.
so,
225 = 81 + x²
as x is also the third side of the triangle.
=> 144 = x²
x = 12 ft