2) Impostando una opportuna proporzione e applicando le proprietà delle proporzioni, risolvi il seguente problema. Determina le lunghezze di due percorsi stradali sapendo che la loro somma è pari a 450 km e che il loro rapporto è uguale \( a \frac{5}{3} \).

Find all x -intercepts of the following function. Write your answer or answers as coordinate points. Be sure to select the appropriate number of \( x \)-intercepts. \[ f(x)=\frac{3 x^{2}-x}{x^{2}-3 x-54} \]

If \( 10^{\log x}=10^{18} \), what is the value of \( x ? \) (1 point) 18 \( 10^{18} \) -18 \( 10^{-18} \)

Find the slope and \( y \)-intercept of the graph of the equation. \[ y=\frac{2}{5} x-1 \] Slope \( =\square \) (Enter a fully reduced fraction.) The y-intercept is \( \square \). (Simplify your answer. Type an ordered pair.)

Use the rule \( \log _{b}(x y)=\log _{b} x+\log _{b} y \) to find \( \log _{2}(16 \cdot 64) \). (1 point)

Solve for \( x \) in the logarithmic equation \( 10^{\log \left(10^{24}\right)}=10^{x} \). (1 point) \( \begin{array}{l}x=10^{24} \\ x=24^{10} \\ x=24 \\ x=10\end{array} \)