PROBLEM FOR CHAMP ONLY… REAL NUMBER level - 3

PROBLEM FOR CHAMP ONLY…

REAL NUMBER

1. Given that a^x = b^y = c^z  and b^2 = ac, then show that y/x – 2z/(x + z) = 0

2. Find the square root of 14 – 6 (5)^1/2

3. If 2^(2x + 4) – 129 x 2^x + 8 = 0, find x.

4. Solve 2^x + 3^y = 5; 2^(x + 2) – 3^(y + 1) = 6 .

5. Find the remainder in the division of 230 / 7

6. Find the remainder when 2^100 + 3^100 + 4^100 is divisible by 7.

7. Show that 2^90 + 3^90 is a multiple of 13.

8. Find the number of divisors of 27 x 38 x 59.

9. Find the sum of the divisors of 900