Yes, ln x = -2 <==> x = e-2, which is approximately 0.135.justin345 said:Homework Statement
Hi!
We know that ln x=y, thus x=e^(y).
If I have ln x=-2, can my x be equal e^(-2)=0.135?
Lnx is a mathematical expression that represents the natural logarithm of x. It is commonly written as ln(x) or loge(x).
This equation means that the natural logarithm of x is equal to -2. In other words, -2 is the power to which the base of the natural logarithm (e) must be raised to get x.
To solve for x, we need to use the inverse of the natural logarithm function, which is e^x. We can rewrite the equation as e^x = e^-2 and then take the natural logarithm of both sides to get x = -2.
Yes, the equation can have multiple solutions, as the natural logarithm function is not a one-to-one function. This means that different values of x can result in the same output of -2.
The equation Lnx=-2 is commonly used in calculus and other fields of mathematics and science to solve for unknown variables in exponential and logarithmic functions. It is also used in modeling and analyzing natural phenomena, such as population growth and decay.