Name: ________________________ Class: ___________________ Date: __________
Logarithms Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Write the equation in logarithmic form.
____
1. 6 4 = 1, 296
a. log 6 1, 296 = 4
b. log 1, 296 = 4
c.
d.
log 1, 296 = 4 ⋅ 6
log 4 1, 296 = 6
c.
log 125 625 =
4
____
2. 125 3 = 625
a.
log 4 625 = 125
3
b.
3 log 4 625 = 125
d.
4
3
3
log 625 125 =
4
Evaluate the logarithm.
____
3. log 5
a.
____
____
1
625
–3
b.
5
c.
–4
d.
4
4. log 3 243
a. 5
b.
–5
c.
4
d.
3
5. log 0.01
a. –10
b.
–2
c.
2
d.
10
c.
(4 + 2) log b (v + x)
Ê
ˆ
log b ÁÁ v 4 + x 2 ˜˜
Ë
¯
Write the expression as a single logarithm.
____
____
6. 4 log b v + 2 log b x
a. log b (v 4 x 2 )
Ê
ˆ
b. log b ÁÁ vx 4 + 2 ˜˜
Ë
¯
7. log 3 4 − log 3 2
a. log 3 2
d.
b.
log 3 2
c.
1
log 2
d.
log 2
ID: A
Name: ________________________
____
ID: A
8. 4 log x − 6 log (x + 2)
x
a. 24 log
x+2
b. log x 4 (x + 2) 6
c.
log x(x + 2) 24
d.
none of these
c.
log 7 2 − log 7 n
d.
−n log 7 2
c.
log 3 11 + 3 log 3 p
d.
11 log 3 p 3
Expand the logarithmic expression.
____
9. log 7
a.
b.
n
2
log 7 n − log 7 2
log7 n
log7 2
____ 10. log 3 11p 3
a. log 3 11 ⋅ 3 log 3 p
b.
____ 11. log b
a.
b.
log 3 11 − 3 log 3 p
57
74
1
1
log b 57 + log b 74
2
2
1
1
log b 57 − log b 74
2
2
c.
d.
log b 57 − log b 74
log b
1
(57 − 74)
2
____ 12. Use the properties of logarithms to evaluate log 3 9 + log 3 36 − log3 4.
a. 2
b. 4
c. 8
d.
41
____ 13. Use the Change of Base Formula to solve 2 2x = 90. Round to the nearest ten-thousandth.
a. 7.6133
b. 9.3658
c. 3.2459
d. 12.9837
____ 14. Solve log(4x + 10) = 3.
7
b.
a. −
4
495
2
c.
250
____ 15. Solve 3 log 2x = 4. Round to the nearest ten-thousandth.
a. 10.7722
b. 5
c. 2.7826
2
d.
990
d.
0.6309
Name: ________________________
ID: A
____ 16. Solve log 3x + log 9 = 0. Round to the nearest hundredth if necessary.
a. 0.33
b. 0.04
c. 3
d.
27
____ 17. Solve log(x + 9) − log x = 3.
a. 0.0090
b. 0.3103
c.
3.2222
d.
111
____ 18. Solve 2 log 4 − log 3 + 2 log x − 4 = 0.
a. 12.3308
b. 43.3013
c.
86.6025
d.
1875
____ 19. The sales of lawn mowers t years after a particular model is introduced is given by the function y =
5500 ln(9t + 4), where y is the number of mowers sold. How many mowers will be sold 2 years after a model
is introduced? Round the answer to the nearest whole number.
a. 37,897 mowers
c. 15,901 mowers
b. 7,383 mowers
d. 17,000 mowers
3