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:
Step-by-step explanation:
Isolate one variable in the system of equations. Use substitution to create a one-variable equation. Then, set the quadratic equation equal to zero and find the discriminant. If the discriminant is negative, then there are no real number solutions. If the discriminant is zero, then there is one real number solution. If the discriminant is positive, then there are two real number solutions.
The inequality would be 50w + 100 >_ 18,000 ( the _ goes under the > but I cannot do that on my phone )
Answer:
12% is the answer for this question
