Subjects algebra

Missing Coordinates

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1. **State the problem:** We are given the equation $$y = 3^x$$ and ordered pairs where one coordinate is missing. We need to find the missing coordinate so that the pair satisfies the equation. 2. **Recall the formula:** The equation relates $x$ and $y$ as $$y = 3^x$$. 3. **Solve for each pair:** **4a.** Given $(2, 9)$, check if $y = 3^x$ holds: $$3^2 = 9$$ Since $9 = 9$, the pair is correct. **4b.** Given $(?, 3)$, find $x$ such that: $$3 = 3^x$$ Take logarithm base 3 on both sides: $$x = \log_3 3 = 1$$ So the missing coordinate is $1$. 4. **Final answers:** - 4a: $(2, 9)$ (given) - 4b: $(1, 3)$ These pairs satisfy the equation $y = 3^x$.