• Optional Exercise

3.Evaluate each of the following in terms of x and y,if it is given that x = log₂3 and y = log ₂5

1. log ₂15


2. log ₂7.5


3. log ₂60


4. log ₂6750

4.Expand the following.

1. log 100


2. log (128 ÷ 628)


3. log x ²y ³z ⁴


4. log (p²q³ ÷ r ⁴)


5. log √ x³ ÷ y²

5. If x ² + y ²= 25xy,then prove that 2log(x +y) = 3log3 + log x + log y.

6. If log x +y ÷3 = 1 ÷ (log x + log y),then find the value of x÷y +y ÷x

7. If (2.3)^x =(0.23)^y =1000,then find the value of 1 ÷x − 1÷y.

8. If 2 ^x+1 = 3^1−x then find the value of x.

9. Is

(i).log 2 rational or irrational ? Justify your answer.

(ii). log 100 rational or irrational ? Justify your answer.

Optional Exercise

[For extensive learning]

1. Can the number 6 ⁿ,n being a natural number, end with the digit 5?Give reasons.


2. Is 7 ×5 ×3 ×2 +3 a composite number ? Justify your answer.


3. Prove that (2 √3 + √5) is an irrational number.Also check whether (2 √3 + √5)(2 √3 − √5) is rational or irrational.


4. If x² + y² = 6xy,then prove that 2log (x +y) = log x + log y + 3 log 2



5. Find the number of digits in 4²⁰¹³,if log ₁₀ 2 =0.3010.

Note:Ask your teacher about integral part and decimal part of the logarithm of a number.