8.6 Natural Logarithms
A man travels the world over in search of what he
needs and returns home to find it.
Do you remember e?
5
e  2.71828
4
5
3
4
2
3
1
2
1
-5 -4 -3 -2 -1
-5 -4 -3 -2 -1
1
-1
-2
-3
-4
-5
2
3
4
5
1
-1
-2
-3
-4
-5
2
3
4
5
Write each expression as a single logarithm (condense).
1
1
2ln12  ln 9
2ln x  3ln y  ln z
ln8  ln x
2
2
Expand each logarithm (expand).
4 x2
ln
7
x2
ln 3 5
yz
Solve the logarithmic equations.
2ln  4m  3  2  28
ln  2 x  4   6
3
Solve the exponential equations.
3e
x 4
 2  38
4e3 x  1.2  14
An initial investment of $200 is now valued at $254.25. The
interest rate is 6%, compounded continuously. How long has
the money been invested?
8.6 Natural Logarithms
HW: #1-9 odd, 14-26 even, 29, 30, 55 – 59 all
A man travels the world over in search of what he
needs and returns home to find it.