Part 3/7:
The exponential function approaches infinity as ( x ) increases and approaches zero as ( x ) decreases into negative values. For logarithmic equations, the domain transforms into a range, now constrained to ( (0, \infty) ), while the range becomes all real numbers. This transformation highlights the symmetry in the graphs of these functions.
Important Properties of Logarithms
Understanding logarithms includes familiarizing oneself with several key properties or laws which can simplify expressions involving logarithmic functions. These laws are crucial for many fields in mathematics.
1. Basic Logarithm Identity
The first fundamental property of logarithms states that:
[
\log_a(a^x) = x
]