Solving equations Solve the following equations.


ln x= -1

Key Concepts

Natural Logarithm

The natural logarithm, denoted as ln, is the logarithm to the base e, where e is approximately 2.71828. It is the inverse function of the exponential function, meaning that if y = ln(x), then x = e^y. Understanding the properties of natural logarithms is essential for solving equations involving ln.

Exponential Function

The exponential function is a mathematical function denoted as e^x, which describes growth or decay processes. It is crucial for solving logarithmic equations, as converting a logarithmic equation to its exponential form allows for easier manipulation. For example, if ln(x) = -1, it can be rewritten as x = e^(-1).

Solving Logarithmic Equations

Solving logarithmic equations involves isolating the variable by converting the logarithmic expression into its exponential form. This process often requires understanding the properties of logarithms, such as the product, quotient, and power rules. In the case of ln(x) = -1, applying the exponential function helps find the value of x.