Division and Distribution into Groups of Equal Sizes

Q. If $a^x=b^y=c^z=d^w,$ then ${\log }_a\left(bcd\right)-x(\frac{1}{y}+\frac{1}{z}+\frac{1}{w})$ is equal to

Q. An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5, and 7. The smallest value of n for which this is possible is

1. 8
2. 6
3. 7
4. 9

Q. An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5, and 7. The smallest value of n for which this is possible is

1. 8
2. 6
3. 7
4. 9