12 ln x=44
ln x=44/12
x=e^(44/12)
[put that in your calc, or in the google search window (google calc).
Well, if we're talking about solving for x, we can start by getting rid of that pesky natural logarithm. But before we do that, let me tell you a joke. Why don't scientists trust atoms? Because they make up everything!
Now, back to business. To get rid of the natural logarithm, we'll need to take the exponential of both sides. So e raised to the power of both sides equals e to the power of 44. But just a warning, e is a bit of a rebel and likes to hang out with irrational numbers.
So, x equals e to the power of 44 divided by 12. And if you're wondering where the clown in me came from, well, it's because solving equations can be a bit of a circus sometimes!
To solve the equation 12 ln x = 44, follow these steps:
Step 1: Divide both sides of the equation by 12 to isolate the natural logarithm term: ln x = 44/12.
Step 2: Simplify 44/12 to get 11/3: ln x = 11/3.
Step 3: Rewrite the equation in exponential form. Since ln x is the logarithm to the base e, we can rewrite the equation as x = e^(11/3).
Step 4: Evaluate e^(11/3) either using a calculator or by using the natural logarithm property: e^(11/3) ≈ 10.27.
Therefore, the solution to the equation 12 ln x = 44 is approximately x ≈ 10.27.
To solve the equation 12 ln x = 44, we need to isolate the variable x.
The equation involves the natural logarithm function, which is denoted by ln. The natural logarithm is the inverse function of exponential growth, often written as log base e. To isolate the variable x, we need to undo the natural logarithm by exponentiating both sides of the equation.
Here's the step-by-step process to solve it:
Step 1: Divide both sides of the equation by 12 to isolate the natural logarithm term:
ln x = 44/12
Step 2: Simplify the right side of the equation:
ln x = 11/3
Step 3: To eliminate the natural logarithm, we need to exponentiate both sides using the base of the natural logarithm, which is e. The exponential form of a logarithm is x = e^y, where x is the variable, e is the base, and y is the exponent. Applying this to our equation:
x = e^(11/3)
Step 4: Evaluate the right side using a calculator or by approximating the value of e:
x ≈ 20.0855
So, the approximate value of x, which satisfies the equation 12 ln x = 44, is x ≈ 20.0855.