Logarithm Properties And Solving Log And Exponential Equations Worksheet

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Review Handout #5:
Name: __________________________ Period _____
This worksheet will give you some more practice involving Logarithm properties and solving Log and
Exponential Equations.
Log Properties:
Product Property:
log
A
log
B
log(
AB
)
A
Quotient Property:
log
A
log
B
log
B
Power Property:
k
log
A
k
(log
A
)
I. SIMPLIFY using log properties (write as a single log expression.) Then solve a-d.
(a)
= ___________________________________________________
log
8
log
16
log
2
4
4
4
(b)
______________________________________________
log
5
log
25
log
125
5
5
5
(c)
__________________________________________________
log
7
log
56
log
8
7
7
7
(d)
_________________________________________________
log
9
log
39
log
13
3
3
3
(e)
= ______________________________________________________
5
log
464
5
log
2
2
2
Hint: use ab+ac=a(b+c) first
(f)
= __________________________________________________
4
log
64
2
(log
16
log
) 4
(g)
= ____________________________________________________
ln(
) 5
2
ln(
) 3
2
ln(
) 4
II. SOLVE. Change to log equations into their equivalent exponential equation.
Round decimal answers to the nearest hundredth
(a) log 216 3
Write as an Exponential Equation: __________________
x
Then solve for x:
x = _______
(b)
Write as an Exponential Equation: __________________
log
16
2
x
Then solve for x:
x = _______
(c)
Write as an Exponential Equation: __________________
log
x
3
5
Then solve for x:
x = _______
(d)
Write as an Exponential Equation: __________________
log
3
x
81
Then solve for x:
x = _______

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