Log_2aa=x    then, a=(2a)^x  ......(1)

Log_3a2a=y    then,2a=(3a)^y ......(2)

Log_4a 3a=z  then, 3a=(4a)^z ......(3)

So, 

a=(2a)^x  [from (1)]

Or, a=(3a)^xy    [from(2)]

Or, a=(4a)^xyz     [from(3)]

Multiplying both sides by 4a,

4a.a=4a.(4a)^xyz  

Or,(2a)² =(4a)^{xyz + 1} 

Or,(3a)^2y =(4a)^xyz+1 

Or,(4a)^2yz =(4a)^xyz+1 

Or, 2yz = xyz+1 .proved.

BODMAS=Bracket, Order, Division, Multiplication, Addition and Subtraction. In certain regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition and Subtraction) is the synonym of BODMAS. It explains the order of operations to solve an expression.

If a vector A is multiplied by a real number (say n), the vector of same nature is obtained but its magnitude is n times that of A.

Program to input any number and display number of odd numbers in it;

#include<stdio.h>

#include<stdlib.h>

#include<conio.h>

#include<string.h>

int main() {

int i, number, num1, num2=0, num3, num4 =0, rem, rem1, rem2, rev = 0;

printf("Enter your number ==> ");

scanf("%d", &number);

num1 = number;

while(num1 != 0) {

rem = num1%10;

rem1 = rem%2;

if (rem1 != 0) {

num2 = num2*10 + rem;

}

num1 /= 10;

}

num3 = num2;

while (num2 != 0) {

...

In benzene molecule, carbon and carbon bond can't have polarity because there is not any electronegativity difference and the carbon hydrogen is also not much polar because the electronegativity difference is almost zero and also the small pull due to small difference in Electronegativity is balanced due to even pull from all directions.

In chlorobenzene the electronegativity difference between carbon and chlorine is very high so, it is polar.

(to compare polarity first check electronegativity...