The Equation: 3^3x – 9 = 18
When we encounter a mathematical equation like 3^3x – 9 = 18, our goal is to find the value of x that satisfies the equation. This type of equation involves exponents and requires algebraic manipulation to solve. Let’s break down the steps to find the solution to this equation.
Solving the Equation Step by Step
- Isolate the Exponential Term: To start solving the equation, we need to isolate the term with the exponent. In this case, we have 3^3x on one side, so we move the constant terms to the other side of the equation.
- Adding 9 to Both Sides: The equation 3^3x – 9 = 18 becomes 3^3x = 27 after adding 9 to both sides.
- Writing 27 as a Power of 3: 27 can be expressed as 3^3, so the equation simplifies to 3^3x = 3^3.
- Setting the Exponents Equal: In exponential equations, when the bases are the same, the exponents are equal. Therefore, we can equate the exponents in this case: 3x = 3.
- Solving for x: To solve for x, we divide both sides by 3. So, x = 1 is the solution to the equation 3^3x – 9 = 18.
Verification of the Solution
After calculating the value of x as 1, it is essential to verify if this solution indeed satisfies the original equation. Let’s substitute x = 1 back into the equation and check if both sides are equal.
Substitute x = 1 into the equation: 3^3(1) – 9 = 18
Calculate the left side: 3^3 – 9 = 27 – 9 = 18
Since the left side equals the right side (18 = 18), we can confirm that x = 1 is the correct solution to the equation.
Conclusion
The solution to the given equation 3^3x – 9 = 18 is x = 1. By following the steps of isolating the exponent, simplifying, equating the exponents, and solving for x, we were able to find the value that satisfies the equation. Additionally, the verification step confirmed the accuracy of our solution.
