Lesson Vocabulary

• natural logarithmic function

Take Note Key Concept: Natural Logarithmic Function

If y = e x , y equals , e to the x , comma  then x = log e y = l n y . x equals , log base e , y equals l n y .  The natural logarithmic function is the inverse of x = x equals  ln y, so you can write it as y = y equals  ln x.

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Problem 1 Simplifying a Natural Logarithmic Expression

What is 2 l n 15 − l n 75 2 l n 15 minus l n 75  written as a single natural logarithm?

2 l n 15 − l n 75 = l n 15 2 − l n 75 Power Property of Logarithms   = l n 15 2 75 Quotient Property of Logarithms   = l n 3 Simplify . table with 3 rows and 3 columns , row1 column 1 , 2 l n 15 minus l n 75 , column 2 equals l n , 15 squared , minus l n 75 , column 3 cap powercap propertyofcap logarithms , row2 column 1 , , column 2 equals l n . fraction 15 squared , over 75 end fraction , column 3 cap quotientcap propertyofcap logarithms , row3 column 1 , , column 2 equals l n 3 , column 3 cap simplify , . , end table