Use propenties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1 . Where possible, evaluate logarithmic expressions. \( \frac{1}{2} \log _{5} x+\log _{5} y \)

Risolvi le seques \( \frac{-x^{2}+7 x-12}{2 x^{2}-7 x+3} \geqslant 0 \)

Add the polynomials: (x^4 + 3x^3 - x) + (2x^4 - 5x^3 + 4).

प्रश्नाबानी 2.2 निम्न द्विघात बहुपदों के शून्यक ज्ञात कीजिए और शून्यकों तथा गुणांकों के बीच के संबंध की सत्यता की जाँच कीजिए : \( \begin{array}{lll}\text { (iv) } x^{2}-2 x-8 & \text { (ii) } 4 s^{2}-4 s+1 & \text { (iii) } 6 x^{2}-3-7 x \\ \text { (iv) } 4 u^{2}+8 u & \text { (v) } s^{2}-15 & \text { (vi) } 3 x^{2}-x-4\end{array} \)

\( 22 \quad \frac { 1 } { 4 } x - \frac { 5 } { 2 } = - 2 \)

D) A student claimed that the largest integer of \( k \) for which the graph \( y=2 x^{2}-3 x+k-1 \) meets the \( x \)-axis is 2 . Verify this statement.