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:
5/2
Step-by-step explanation:
Since the two figures are similar therefore their sides are in proportion.
for the first one
factor=2/8=1/4
for the second
factor=10/4=5/2
I hope this helps :)
Answer:
9,498.5 ft²
Step-by-step explanation:
110 ft = circumference (C)
C=2r
110=2r
110/2=2r/2
55=r
Area of a circle (A) = πr²
Use 3.14 for π
A=3.14(55)²
A=3.14(3025)
A=9,498.5
The area of the garden is 9,498.5 ft²
The unit rate is 75¢. 7.50 divided by 10 (oranges) is the $0.75 or 75¢
Rule: add 4/6 because 5/6 + 4/6=1 1/2
