Exam 4c - Logarithmic & Exponential Functions Worksheet Page 3
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4MAC 1105 - College Algebra
7
11) ln
e
11)
1
e
A) 7e
B)
C)
D) 7
7
7
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
12) log 3 (7 · 11)
12)
A) log 3 77
B) log 3 7 + log 3 11
C) ( log 3 7)( log 3 11)
D) log 3 7 - log 3 11
13) log (100x)
13)
A) 2log x
B) 2x
C) 20 + log x
D) 2 + log x
e 5
14) ln
14)
2
A) ln e 5 - ln 2
D) ln e 5 + ln 2
B) 5 - ln 2
C) 5 + ln 2
x 3
15) log 3
15)
y 8
3
x
A)
log
(
)
B) 3 log 3 x + 8 log 3 y
3
8
y
C) 8 log 3 y - 3 log 3 x
D) 3 log 3 x - 8 log 3 y
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose
coefficient is 1. Where possible, evaluate logarithmic expressions.
1
16)
(log 3 x + log 3 y) - 4 log 3 (x + 10)
16)
7
7
7
7
7
7
x +
y
xy
xy
x + y
A) log 3
B) log 3
C) log 3
D) log 3
(x + 10) 4
(x + 10) 4
4(x + 10)
(x + 10) 4
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
17) log 12 84.3
17)
A) 1.7845
B) 3.0050
C) 0.8466
D) 0.5604
Solve the equation by expressing each side as a power of the same base and then equating exponents.
18) 4 (1 + 2x) = 1024
18)
A) {-2}
B) {256}
C) {8}
D) {2}
19) 32 x = 8
19)
3
3
5
A)
B)
C)
D) 3
5
4
3
3
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