Solve 14 - ln(2-x)=0. solve for x
-ln(2-x)=-14
ln 1/(2-x)=-14
1=-14(2-x)
1=-28+14x
29=14x
29/14=x
not sure where I'm going wrong
or
ln (2-x) = 14
e^{ln(2-x) = 2-x
so
2-x = e^14
x = 2 - e^14
x = - 1202602
You need to remove the natural log by writing both sides of the equation to base ''e''.
e^{ln(2-x)} = e^14
Applying the law of logarithms on the LHS:
2 - x = e^14
So:
x = 2 - e^14
To solve the equation 14 - ln(2-x) = 0 for x, you need to isolate the variable x. Let's go through the steps again:
1. Start with the equation: 14 - ln(2-x) = 0
2. Subtract 14 from both sides of the equation to get rid of the constant term on the left side:
- ln(2-x) = -14
3. Take the inverse of the natural logarithm function (e^x) on both sides of the equation to cancel out the ln:
e^(- ln(2-x)) = e^(-14)
4. Use the property that e^(ln(x)) = x to simplify the left side of the equation:
2-x = e^(-14)
5. Subtract 2 from both sides of the equation to isolate -x:
-x = e^(-14) - 2
6. Finally, multiply both sides of the equation by -1 to solve for x:
x = -1 * (e^(-14) - 2)
So, the solution for x is x = -1 * (e^(-14) - 2).
Make sure to use a calculator or computer program that can compute exponentiation and subtraction accurately to get the numerical value of x.