1. The problem asks for the coordinates of the point of intersection of the two graphs: $y = \log_5 x$ and $y = \log_7 x$. 2. At the point of intersection, the $y$-values are equal, so we set the equations equal to each other: $$\log_5 x = \log_7 x$$ 3. Using the change of base formula, $\log_a b = \frac{\ln b}{\ln a}$, rewrite both sides: $$\frac{\ln x}{\ln 5} = \frac{\ln x}{\ln 7}$$ 4. Multiply both sides by $\ln 5 \cdot \ln 7$ to clear denominators: $$\ln x \cdot \ln 7 = \ln x \cdot \ln 5$$ 5. Subtract $\ln x \cdot \ln 5$ from both sides: $$\ln x \cdot \ln 7 - \ln x \cdot \ln 5 = 0$$ 6. Factor out $\ln x$: $$\ln x (\ln 7 - \ln 5) = 0$$ 7. For this product to be zero, either $\ln x = 0$ or $\ln 7 - \ln 5 = 0$. 8. Since $\ln 7 \neq \ln 5$, the only solution is: $$\ln x = 0 \implies x = e^0 = 1$$ 9. Substitute $x=1$ back into either function to find $y$: $$y = \log_5 1 = 0$$ 10. Therefore, the coordinates of the point of intersection are: $$(1, 0)$$