Given:
The equation is:
[tex]3^x\times 9=3^{2n-1}[/tex]
To find:
The value of n in terms of x.
Solution:
We have,
[tex]3^x\times 9=3^{2n-1}[/tex]
It can be written as
[tex]3^x\times 3^2=3^{2n-1}[/tex]
[tex]3^{x+2}=3^{2n-1}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
On comparing the exponents, we get
[tex]x+2=2n-1[/tex]
Add 1 on both sides.
[tex]x+2+1=2n-1+1[/tex]
[tex]x+3=2n[/tex]
Divide both sides by 2.
[tex]\dfrac{x+3}{2}=n[/tex]
Therefore, the value of n is terms of x is [tex]n=\dfrac{x+3}{2}[/tex].
