e^(-X/2)=12
do i bring the (-x/2) down by ln? how do i procede after that?
thanks
e^(-x/2) = 12
(-x/2) = ln12
-x = ln12 * 2
x = -(ln12 * 2)
can you a also help me with this one?
x^2ln(x)=ln(x)
thanks
x^2 = ln(x)/ln(x)
x^2 = 1
x = +/-1
To solve the equation e^(-x/2) = 12, you're on the right track. You need to use the natural logarithm (ln) to isolate x.
1. Start with the equation: e^(-x/2) = 12
2. Apply the natural logarithm (ln) to both sides to remove the exponential function: ln(e^(-x/2)) = ln(12)
3. Using the property of logarithms, the ln and e^x functions cancel out, leaving you with: -x/2 = ln(12)
4. Multiply both sides of the equation by -2 to isolate x: -2 * (-x/2) = -2 * ln(12)
5. Simplify: x = 2 * ln(12)
For the equation x^2ln(x) = ln(x), follow these steps:
1. Start with the equation: x^2ln(x) = ln(x)
2. Divide both sides of the equation by ln(x): x^2 = ln(x)/ln(x)
3. Simplify the right side of the equation: x^2 = 1
4. Take the square root of both sides to solve for x: x = +/- √1
5. Simplify further: x = +/- 1