Logarithm Worksheet With Answer Key - Blake Farman, University Of South Carolina Page 3
ADVERTISEMENT
1
2
3
4
5MATH 111:
HOMEWORK 08 SOLUTIONS
3
(b) Using the law for division we have
160
5
log
(160)
log
5 = log
= log
(32) = log
(2
) = 5.
2
2
2
2
2
5
(c) Using the law for exponents we have
1
1/2
6
1/2
6/2
3
log
(64) =
log
(64
) =
log
((2
)
) =
log
(2
) =
log
(2
) =
3.
2
2
2
2
2
2
12. Use the laws of logarithms to expand the given expression.
x
(a) log
,
5
2
(b) log
(x y).
3
Solution. (a) Using the law for division we have
x
log
= log
(x)
log
(2).
5
5
5
2
(b) Using the law for products and then the law for exponents we have
log
(y)
1/2
1/2
3
log
(x y) = log
(xy
) = log
(x) + log
(y
) = log
(x) +
.
3
3
3
3
3
2
14. Use the laws of logarithms to expand the given expression.
(a) log
(5a),
3
2a
(b) log
.
5
b
Solution. (a) Using the law for products we have
log
(5a) = log
(5) + log
(a).
3
3
3
(b) Using the law for division, then the law for products we have
2a
log
= log
(2a)
log
(b) = log
(2) + log
(a)
log
(b) .
5
5
5
5
5
5
b
16. Use the laws of logarithms to expand the given expression.
2
10
(a) log
(w
z)
10
3
wz
(b) log
7
x
Solution. Using the laws of logarithms we have
(a)
2
10
2
10
10
log
(w
z)
= (log
(w
) + log
(z))
= (2 log
(w) + log
(z))
.
10
10
10
10
10
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education