Explain how you solve the problem of [tex]$3^{x+1}=3^3$[/tex].
Answer (2)
We have the equation 3 x + 1 = 3 3 .
Since the bases are equal, we equate the exponents: x + 1 = 3 .
Solve for x : x = 3 − 1 .
The solution is 2 .
Explanation
Understanding the Problem We are given the equation 3 x + 1 = 3 3 . Our goal is to find the value of x that satisfies this equation.
Equating the Exponents Since the bases are the same (both are 3), we can set the exponents equal to each other. This gives us the equation x + 1 = 3 .
Solving for x Now, we solve for x by subtracting 1 from both sides of the equation: x + 1 − 1 = 3 − 1 x = 2
Final Answer Therefore, the solution to the equation 3 x + 1 = 3 3 is x = 2 .
Examples
Imagine you are baking a cake and need to increase the recipe. If the original recipe calls for 3 x + 1 cups of flour and you want to triple the recipe to 3 3 cups, solving this equation helps you determine how much to adjust the exponent (amount of flour) to get the desired result. Understanding exponential equations is crucial in various scaling and growth scenarios.
To solve the equation 3 x + 1 = 3 3 , we equate the exponents since the bases are the same, resulting in the equation x + 1 = 3 . By solving for x, we find that x = 2 . Therefore, the solution is x = 2 .
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