Math 1020
Quiz 6
Name___________________________________
Use properties of logarithms to expand the logarithmic expression as much as possible.
1) log 5 (25x)
2) log
3) ln
x
10
1)
2)
e2
9
3)
4) logn x5
4)
5) logb (yz 4 )
5)
x
6) log 5
125
6)
7) log 2
x2
y7
7)
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.
8) log c m + log c n
8)
9) 3 log b m - log b n
9)
10) 3 log x 2 + log x 3
10)
11) log 2 48 - log 2 3
11)
1
12)
1
(log8 x + log8 y)
3
12)
Solve the equation by expressing each side as a power of the same base and then equating exponents.
1
13) 2 (3x + 7) =
13)
4
14) 81x =
1
3
14)
Solve the exponential equation. Express the solution set in terms of natural logarithms.
x+8
=7
15) 4
16) e
x+5
=2
15)
16)
17) 4 x + 4 = 5 2x + 5
17)
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
18) log 3 (x + 1) = 2
18)
19) log 6 (x + 2) = -1
19)
20) ln 4 + ln (x - 1) = 0
20)
2
Answer Key
Testname: MATH 1020 QUIZ 6
1) 2 + log 5 x
2) log x - 1
3) 2 - ln 9
4) 5logn x
5) logb y + 4 logb z
1
6) log 5 x - 3
2
7) 2 log 2 x - 7 log 2 y
8) log c (mn)
m3
9) log b
n
10) log x 24
11) 4
3
12) log8 xy
13) {-3}
1
14) 8
15)
ln 7
-8
ln 4
16) {ln 2 - 5}
5 ln 5 - 4 ln 4
17)
ln 4 - 2 ln 5
18) {8}
19) -
11
6
5
20) { }
4
3