7.6 The Natural Base, e
e = 2.71828..., the Base of Natural Logarithms e ­ a real, irrational number constant that appears in some kinds of mathematics problems.
Ex: problems involving growth or decay (including compound interest), the statistical "bell curve," the shape of a hanging cable (or the Gateway Arch in St. Louis), some problems of probability, some counting problems, and the study of the distribution of prime numbers.
Natural logarithm
­ log with a base of e.
­ is abbreviated as "ln" (instead of log ).
All properties for logs are true for logs with base e.
The natural logarithmic function f(x)=ln(x) is the inverse of the
natural exponential function f(x)=ex.
Simplify
2) e3 ln(x+1)
0.15t
1) ln(e
)
3) ln e2x + ln ex
4) ln5 + 2lnx
5) 3ln(x) ­ ln(y) + ln(z)
Expand:
1) ln(3x/y)
Ex: Solve, round to the nearest hundredth.
1) 18=5e0.4k+2
2) ln5­lnx=3
Assignment
7.6 Worksheet