Name_______________________________________ Date__________________ Period____________
A10-Condensing Logs
Write each expression as a single logarithm. The answer to each problem can be found in the answer box on the
bottom. SHOW ALL STEPS!!
1. log 𝑥 + 7 log 𝑦
2. 6 log 𝑥 − 3 log 𝑥
3. 6 log 𝑥 − log 𝑥
4. log 3 𝑥 + log 3 𝑦
𝑥
𝑦2
7. log (𝑦) + log ( 𝑥 )
1
10. 2 (4 log 3 3 + log 3 𝑥)
1
1
5. 2 log 3 𝑥 − log 3 𝑦
6. 2 log 𝑥 + 2 log 𝑦
8. 3(2 log 3 𝑥 − log 3 𝑦)
9. 2(log 𝑥 + 4 log 𝑥)
11. (log 3 𝑥 + log 3 𝑦) − log 3 𝑧
12. 4(log 3 𝑥 − log 3 𝑦)
13. 12 log 3 𝑥 − (16 log 3 𝑦 + 12 log 3 𝑧)
14. (8 log 𝑥 + 12 log 𝑦) − 2 log 𝑧
Answers: Not all answers will be used, but no answers is repeated.
𝑥6
𝑥 2𝑦2
)
𝑧2
𝑥𝑦
𝑥4
log (
log 3 ( 𝑧 )
log(𝑥 3 )
log 3 (𝑦4 )
log ( 𝑦4 )
log √𝑥𝑦
log(𝑦)
log 3 (8𝑥 3 )
log 3 (𝑥𝑦)
log 3 (𝑥 2 )
log 3 (9√𝑥)
log(𝑥 10 )
log 3 (𝑦3 )
𝑥 12
𝑥 8 𝑦 12
)
𝑧2
log(𝑥 5 )
log(
log 3 (𝑦16 𝑧12 )
log 3 √𝑥𝑦𝑧
log(𝑥𝑦 7 )
log(𝑥𝑦𝑧)
log 3 ( 𝑦 )
𝑥 12
𝑥2
log 3 √𝑥𝑦