The definition of a logarithm says. Product Notation Induction Logical Sets. Apparently the notation ln first appears in Stringhams book Uniplanar algebra.
The notation above would be read as log to the base b of N equals x means that b to the x power equals N.
The word logarithm was invented by John Napier in 1614. Of course from the equation x at we deduce that t log x where the log is to base a but this involves a much later way of thinking. Being part I of a propaedeutic to the higher mathematical analysis. In this segment we will cover equations with logarithms.