Answered

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

A. [tex]\( x = -11 \)[/tex]
B. [tex]\( x = -7 \)[/tex]
C. [tex]\( x = 7 \)[/tex]
D. [tex]\( x = 11 \)[/tex]

Sagot :

GinnyAnswer
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]
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