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Section 3.3 Properties of Logarithms 215
3. (a)
log 15 x
(b) log 15 x
log 10 x
log 10 15 log 10 x
log 10 5
ln x
ln 15 ln x
ln 5
4. (a)
log 13 x
(b) log 13 x
log 10 x
log 10 13 log 10 x
log 10 3
ln x
ln13 ln x
ln 3
5. (a)
log a 3 10 log 10310
log 10 a
(b) log a 3 10 ln310
ln a
6. (a)
log a 3 4 log 1034
log 10 a
(b) log a 3 4 ln34
ln a
7. (a)
log 2.6 x log 10 x
log 10 2.6
(b) log 2.6 x ln x
ln 2.6
8. (a)
log 7.1 x log 10 x
log 10 7.1
(b) log 7.1 x ln x
ln 7.1
9. log 3 7 ln 7
ln 3 1.771
10. log 7 4 ln 4
ln 7 0.712
11. log 12 4 ln 4
log 18 64
ln 64
ln18
13. log 9 0.8 ln0.8
ln 9 0.102
ln 12 2 12.
ln 82
ln 8 2
14.
log 3 0.015 ln0.015
ln 3
3.823
15. log 15 1460
ln 1460
ln 15 2.691
ln 135
16. log 20 135 1.637
ln 20
17.
ln 20 ln4 5 18.
ln 4 ln 5
ln 500 ln5 3 4 19.
ln 5 3 ln 4
ln 5
64 ln 5 ln 64
ln 5 ln 4 3
3 ln 5 ln 4
ln 5 3 ln 4
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20.
22.
24.
ln 2 5 ln 2 ln 5 21. log b 25 log b 5 2
ln 4 12 ln 5
2 log b 5
ln 4 ln 5
20.8271 1.6542
1 2
log b 30 log b 2 3 5 23.
log b
3 1 2 log b 3
log b 2 log b 3 log b 5
1 20.5646
0.3562 0.5646 0.8271 1.7479
0.2823
log b 25 9 log b 5 2 log b 3 2
2 log b 5 2 log b 3
20.8271 20.5646 0.5250