The notation $x = \ln y$ is a shorthand for the natural logarithm to the base $e$: $x = \log_{e} y$ . This notation is used throughout mathematics, science, and engineering.
The shorthand notation $x = \log y$ is sometimes used when the base $b$ remains fixed and is understood from the context. The “understood” base, however, can vary from place to place:
$x = \log y$ often means $x = \ln y$ in mathematics texts.
$x = \log y$ often means $x = \lg y$ in science and engineering texts.
$x = \log y$ often means $x = \log_{2} y$ in computer science texts.
Be careful when reading or using $x = \log y$ .