You can apply that again to the product [1/(2√xi)]*[e^(-θ√xi)]. You can then also use ln(xa) = a ln(x) for cases like a = -1, a = 1/2. What can you do with ln(ex)?Phox said:= nlnθ + Ʃln(1/(2√xi)*e^(-θ√xi))
Ok so from what I understand the ln of a product is the sum.
Phox said:Homework Statement
L(θ) = ∏(θ/(2√xi)*e^(-θ√xi)),i=1, n
Homework Equations
The Attempt at a Solution
-> θ2∏(1/(2√xi)*e^(-θ√xi))
taking natural log of both sides
lnL(θ) = nlnθ + ln∏(1/(2√xi)*e^(-θ√xi))
= nlnθ + Ʃln(1/(2√xi)*e^(-θ√xi))
Ok so from what I understand the ln of a product is the sum. But I'm not sure how exactly to simplify from here
The natural log of a product is the logarithm of the product of two or more numbers to the base of the mathematical constant e, also known as the natural logarithm. It is denoted as ln(x * y) or ln(xy).
The natural log of a product can be calculated by taking the natural log of each individual number in the product and then adding them together. For example, ln(2 * 3) = ln(2) + ln(3).
The natural log of a product is equal to the sum of the natural logs of its factors. This relationship is known as the logarithmic product rule, which states that ln(xy) = ln(x) + ln(y).
The natural log of a product is important in mathematics and science because it helps simplify complex calculations involving products, such as calculating compound interest or solving exponential equations. It is also used in various mathematical and scientific models and formulas.
Yes, the natural log of a product can be negative. This occurs when one or more of the factors in the product is between 0 and 1, as the natural log of numbers between 0 and 1 is negative. For example, ln(0.5 * 2) = ln(0.5) + ln(2) = -0.693 + 0.693 = 0.