What is the value of [tex]$x$[/tex] if [tex]$5^{x+2}=5^9$[/tex]?

A. [tex][tex]$x=-11$[/tex][/tex]
B. [tex]$x=-7$[/tex]
C. [tex]$x=7$[/tex]
D. [tex][tex]$x=11$[/tex][/tex]



Answer :

To find the value of [tex]\( x \)[/tex] in the equation [tex]\( 5^{x+2} = 5^9 \)[/tex], follow these steps:

1. Understand the properties of exponents: When the bases are the same, you can set the exponents equal to each other. This principle comes from the property of exponents that states if [tex]\(a^m = a^n\)[/tex], then [tex]\(m = n\)[/tex], provided that [tex]\(a\)[/tex] is a non-zero number.

2. Apply this property to the given equation:
[tex]\[ 5^{x+2} = 5^9 \][/tex]
Since the bases ([tex]\(5\)[/tex]) are the same, we can equate the exponents:
[tex]\[ x + 2 = 9 \][/tex]

3. Solve for [tex]\( x \)[/tex]:
[tex]\[ x + 2 = 9 \][/tex]

4. Subtract 2 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[ x = 9 - 2 \][/tex]

5. Calculate the result:
[tex]\[ x = 7 \][/tex]

Thus, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( 5^{x+2} = 5^9 \)[/tex] is [tex]\( \boxed{7} \)[/tex].