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]
Answer (2)
The value of x is 7 .
Explanation
Understanding the Problem We are given the equation 5 x + 2 = 5 9 . Our goal is to find the value of x that satisfies this equation. Since the bases on both sides of the equation are the same (both are 5), we can equate the exponents. This means that x + 2 must be equal to 9.
Solving for x Now we have a simple equation to solve: x + 2 = 9 . To isolate x , we need to subtract 2 from both sides of the equation. This gives us: x = 9 − 2 .
Finding the Value of x Performing the subtraction, we find that x = 7 . Therefore, the value of x that satisfies the original equation is 7.
Examples
Imagine you're baking a cake and need to adjust the recipe. If the original recipe calls for 5 2 tablespoons of sugar, but you want to make a larger cake that requires 5 9 tablespoons, you need to figure out how much more sugar to add. This problem is analogous to solving the equation 5 x + 2 = 5 9 , where x represents the additional amount needed. Understanding exponential equations helps in scaling recipes and adjusting quantities in various real-life scenarios.
The value of x in the equation 5 x + 2 = 5 9 is 7 . Therefore, the correct answer is option C. This was derived by equating exponents since the bases are the same and solving for x .
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