Exponential & Logarithmic Equations Worksheet With Answers - Math 11009, Section 5.3
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8MATH 11009:
Exponential & Logarithmic
Equations Section 5.3
x
Exponential Function: If b > 0, b = 1, then the function f (x) = b
is an exponential
function. The constant b is called the base of the function and the variable x is the
exponent.
Logarithmic Function: For x > 0, b > 0, and b = 1, the logarithmic function to base
y
b is y = log
x which is defined by x = b
.
b
* Remember ln x is a logarithmic function with base e.
* Remember log x is a logarithmic function with base 10.
Basic Properties of Logarithms: For b > 0, b = 1, we have
x
log
b = 1
log
b
= x
b
b
log x
log
1 = 0
b
= x
b
Logarithmic Properties using base 10 and base e.
log 10 = 1
ln e = 1
log 1 = 0
ln 1 = 0
x
x
log 10
= x
ln e
= x
log x
ln x
10
= x
e
= x
Example 1. Use the properties of logarithms to evaluate the following.
5
(a) ln e
(b) 7 log
24
7
4
(c) log 10
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