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Answer :
The solution to the equation [tex]\(5^{x+2} = 3125\) is \(x = 3\).[/tex]
To solve the equation [tex]\(5^{x+2} = 3125\)[/tex], we need to find a common base for both sides of the equation.
Notice that [tex]\(3125 = 5^5\).[/tex]
So, we can rewrite the equation as:
[tex]\[5^{x+2} = 5^5\][/tex]
Now, since the bases are the same, we can equate the exponents:
x + 2 = 5
Now, we can solve for x:
x = 5 - 2
x = 3
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