Laws of Logarithm Express as a single logarithm. 1. log 3 d − log 3 f + log 3 g − log 3 h 2. 3 − log 3 r 1
3. 2 log 2 m + log 2 n 2
a
a
4. log − 2 log b
b
Expand the single logarithm to a combination of logarithms. 5. log 3 5x 2 6. log 5 xy 7. log 2
8. log 4
3x 2
y
ab
5c
Solve for x: 9. log 7 x = log 7 4 + log 7 3 − log 7 2 10. log 3 x = 4 log 3 2 + log 3 5 − log 3 4 1
11. log 5 x = log 5 9 + log 5 ( x − 1) 2
12. log 6 ( x − 6 ) − log 6 3 = log 6 2 13. log 7 3x 2 = 2 log 7 24 − log 7 3 14. 2 log m ( x + 1) − log m 4 = 0