section_path: Definition
section_name: Definition
paragraph_text: Definition
  
  Given a positive real number b such that b ≠ 1, the logarithm of a positive real number x with respect to base b is the exponent by which b must be raised to yield x. In other words, the logarithm of x to base b is the unique real number y such that b y = x {\displaystyle b^{y}=x}.
  
  The logarithm is denoted " log x " (pronounced as "the logarithm of x to base b ", "the base- b logarithm of x ", or most commonly "the log, base b, of x ").
  
  An equivalent and more succinct definition is that the function log is the inverse function to the function x ↦ b x {\displaystyle x\mapsto b^{x}}.