Answer:
Option 2 - 4
Step-by-step explanation:
Given : Equation [tex]2401=7^{6-2x}[/tex]
To find : What is the power of 7 is 2401
Solution :
We will factorize the 2401 so that we get which number power is 2401
[tex]2401=7\times 7\times 7\times 7[/tex]
[tex]2401=7^4[/tex]
From this we directly know but we find the value of x
Substitute this in the equation :
[tex]7^4=7^{6-2x}[/tex]
If base is same then power equate,
[tex]x^m=x^n\Rightarrow m=n[/tex]
[tex]4=6-2x[/tex]
[tex]2x=2[/tex]
[tex]x=1[/tex]
Substitute in equation,
[tex]2401=7^{6-2(1)}[/tex]
[tex]2401=7^{4}[/tex]
Therefore, Option 2 is correct.
