Question

What should be the index of x so that the value of x so that it's value will be equal to 1?

Don't spam okie​

Answer 1

In our ordinary division, we are clear about the division of a number by the same number. The quotient is always 1 in such case.

For example:-

Divide 4 by 4.

Here,

`(4)/(4) = 1`

Now let solve the above examples by using the laws of indices.

`(4)/(4) = {4}^(1 - 1) = {4}^(0) = 1`

Similarly,

`\frac{ {x}^(m) }{ {x}^(m) } = {x}^(m - m) = {x}^(0) = 1`

Thus,any base with zero index is equal to 1.

Answer 2

We need to tell the index of x for which x will be 1 , First of all , always remember that index of a number means power of the number or to which power it's raised to, like in 2³ , 2 is raised to 3 so 3 is the index. Also we knows an identity i.e

• 
  `{\boxed{\bf{(a^m)/(a^n)=a^(m-n)}}}`

Let's put , m = n

`{:\implies \quad \sf (a^m)/(a^m)=a^(m-m)}`

`{:\implies \quad \boxed{\bf{a^(0)=1}}}`

Also , you should note that for a = 0 , the given expression becomes 0⁰ ,which is not defined , so the above expression is true only for
`{\bf{a\in (-\infty,0)\cup (0,\infty)}}`

Now , as we can replace variables , so , if we replace a by x , we get x⁰ = 1 .

Hence , the required index is 0