Certainly! Let's solve the equation step-by-step:
We start with the given equation:
[tex]\[ 5^{x+2} = 5^9 \][/tex]
Since the bases on both sides of the equation are the same (both are 5), we can equate the exponents. Therefore, we get:
[tex]\[ x + 2 = 9 \][/tex]
Next, we need to solve for [tex]\( x \)[/tex]. We do this by isolating [tex]\( x \)[/tex] on one side of the equation. Subtract 2 from both sides:
[tex]\[ x + 2 - 2 = 9 - 2 \][/tex]
This simplifies to:
[tex]\[ x = 7 \][/tex]
Therefore, the correct value of [tex]\( x \)[/tex] is:
[tex]\[ \boxed{7} \][/tex]
So the correct answer is:
[tex]\[ x = 7 \][/tex]
