Logarithm worksheet for math students

Here are some important and varied types of questions on logarithms, suitable for high school or college-level students:

Basic Level

1. Simplify:
   log⁡101000log101000

2. Solve for xx:
   log⁡2x=5log2x=5

3. Express in terms of logs:
   log⁡b(x2y3)logb(x2y3)

4. Change the base:
   Convert log⁡28log28 to base 10.

Intermediate Level

5. Evaluate:
   log⁡5125+log⁡525log5125+log525

6. Solve for xx:
   log⁡(x)+log⁡(x−1)=1log(x)+log(x−1)=1

7. If log⁡2=0.3010log2=0.3010, log⁡3=0.4771log3=0.4771, find:
   log⁡(18)log(18)

8. Write as a single logarithm:
   2log⁡x−log⁡y+log⁡z2logx−logy+logz

Advanced Level

9. Solve for xx:
   3log⁡3(x+1)=2x3log3(x+1)=2x

10. If a=log⁡102a=log102 and b=log⁡103b=log103, express log⁡10(12)log10(12) in terms of aa and bb.

11. Solve for xx:
    log⁡2(x−1)+log⁡2(x+1)=3log2(x−1)+log2(x+1)=3

12. Find the domain of:
    f(x)=log⁡(x2−4)f(x)=log(x2−4)