Question

Please help me with this

Answer 1

Given:

The equation is:

`3^x* 9=3^(2n-1)`

To find:

The value of n in terms of x.

Solution:

We have,

`3^x* 9=3^(2n-1)`

It can be written as

`3^x* 3^2=3^(2n-1)`

`3^(x+2)=3^(2n-1)`
`[\because a^ma^n=a^(m+n)]`

On comparing the exponents, we get

`x+2=2n-1`

Add 1 on both sides.

`x+2+1=2n-1+1`

`x+3=2n`

Divide both sides by 2.

`(x+3)/(2)=n`

Therefore, the value of n is terms of x is
`n=(x+3)/(2)`.