Given:
[tex]5^2\times 5^{x-5}=625[/tex]
To find:
The value of x.
Solution:
We have,
[tex]5^2\times 5^{x-5}=625[/tex]
It can be written as
[tex]5^2\times 5^{x-5}=5\times 5\times 5\times 5[/tex]
Using property of exponents, we get
[tex]5^{2+x-5}=5^4[/tex] [tex][\because a^m\times a^n=a^{m+n}][/tex]
[tex]5^{x-3}=5^4[/tex]
Comparing the exponents on both sides, we get
[tex]x-3=4[/tex]
Adding 3 on both sides, we get
[tex]x=4+3[/tex]
[tex]x=7[/tex]
Therefore, the value of x is 7.
