Math 1525 Exponential And Logarithmic Functions Worksheet - The Math Department
ADVERTISEMENT
1
2Math 1525
Review Supplement sheet on Exponential and Logarithmic Functions
The definition of an exponential function is as follows:
x
For a>0 and a≠1, the exponential function with base a is f(x) = a
. (usually the base we will use in this class
x
is a = e where e = 2.71828 .This function is called the natural exponential function y=e
)
The inverse function of the exponential function is the logarithmic function. These two functions are related
d
as follows: If m = a
then log
m = d ( this is read log to the base a of m is d.) Again we usually use the
a
natural base e so log
x = lnx.
e
The following properties are important to remember:
1)
m
n
m+n
(a
)( a
) = a
m
n
am-n
2) a
/a
=
0
3) a
=1
-n
n
4) a
= 1/a
√a
1/n
n
5) a
=
6) ln(nm) = ln n + ln m
7) ln(n/m) = ln n – ln m
r
8) ln (n
) = r(ln n)
9) ln e = 1
10) ln 1 = 0
m
11) ln e
= m
ln m
12) e
= m
The above properties can be used to simplify a problem before you try to solve it.
Practice Problems:
n
1. Use the relationship that if m = a
then log
m = n to solve for x.
a
a) log
25 = 2
b) log
x = 1/2
x
36
c) log
64 = x
d) log
(4x-4) = 2
4
x
2. Solve each of the following for x by either taking the natural log or exponential of both sides. Leave
answers in log or exp form.
x+2
a) e
= 5
b) ln(2x+1) = 5
x
c) 3
= 4
3. Simplify the following using the laws of Logarithms:
4
Example: Given the function ln[(x-2)(x+3)
]. You can simplify this function
using the above rules to get ln(x-2) + 4ln(x+3).
Example: ln[(x-2)/(x+5)] = ln(x-2) – ln(x+5)
3
4
a) Simplify
ln [x
(x+1)/(x+2)
] =
2
4. Express the following as a single log form:
ln(3x) + ln(x – 4) – 5ln( x
+ 3) =
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education