Question

Please help me with this

Answer 1

Given:

The equation is:

$3^x\times 9=3^{2n-1}$

To find:

The value of n in terms of x.

Solution:

We have,

$3^x\times 9=3^{2n-1}$

It can be written as

$3^x\times 3^2=3^{2n-1}$

$3^{x+2}=3^{2n-1}$                $[\because a^ma^n=a^{m+n}]$

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.

$\dfrac{x+3}{2}=n$

Therefore, the value of n is terms of x is $n=\dfrac{x+3}{2}$.