Write x in terms of e: ln x^2 = 8.
Is it e^2√2 = x?
Only if you say it is.
x is usually used to represent a variable that can have a wide range of values.
lnx^2 = 8.
e^8 = x^2,
Take sqrt of both sides:
e^4 = x.
Or x = e^4.
No, the expression e^2√2 = x is not a correct expression for x in terms of e in the given equation ln x^2 = 8.
To find x in terms of e, we need to use the properties of logarithms. In this case, we can start by rewriting the equation ln x^2 = 8 as:
2ln x = 8
Next, we can isolate ln x by dividing both sides of the equation by 2:
ln x = 4
Now, we can convert the natural logarithm equation to exponential form by applying the definition of the logarithm:
x = e^4
So, the correct expression for x in terms of e is x = e^4.
To solve the equation "ln x^2 = 8" for x in terms of e, we need to use the properties of logarithms. Because the natural logarithm (ln) is the inverse of the exponential function with base e, we can rewrite the equation as an exponential equation.
First, we can rewrite the equation as: x^2 = e^8.
Next, taking the square root of both sides, we get: x = ±√(e^8).
So, yes, you are correct that x can be written as ±√(e^8), but it can also be simplified further. We can use the fact that √(a^b) = a^(b/2) to simplify the expression.
Therefore, x = ±(e^8)^(1/2) = ±(e^4).
Hence, a more simplified expression for x in terms of e is x = ±e^4.