How do you solve sin(e^x)=0 for x?
The question is "find the smallest number x such that sin(e^x)=0".... but I can't even get AN answer lol!
Much appreciated!
see other post.
To solve the equation sin(e^x) = 0 for x, you need to find the values of x that make the function equal to zero. Here's how you can do it:
1. Start by taking the inverse sine (also known as arcsin) of both sides of the equation: arcsin(sin(e^x)) = arcsin(0). This step helps in eliminating the sine function.
2. Since the range of the arcsin function is between -π/2 and π/2, you can rewrite the equation as e^x = kπ, where k is an integer.
3. To isolate x, take the natural logarithm (ln) of both sides: ln(e^x) = ln(kπ).
4. Simplify the equation, as ln(e^x) = x: x = ln(kπ).
K π is a general representation of all the possible solutions, so you can replace kπ with any integer multiple of π to find all the solutions.
If you want to find the smallest positive x, you can substitute different values for k until you find the smallest x that satisfies the equation. Remember that e^x is always positive, so the expression inside the natural logarithm is positive.