\( \left. \begin{array} { l }{ - ( \frac { 2 } { 5 } ) ^ { 2 } = \square } \\ { \frac { 4 ^ { 3 } } { 5 } = \square } \end{array} \right. \)

Find the domain of the given function and state in Interval notation. \( f(x)=\frac{\sqrt{x-1}}{x-8} \) Domain:

Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. \( \log _{\mathrm{b}}\left(\frac{x^{3} y}{z^{7}}\right) \)

Q2. a). Find an irrational number that lies between \( \begin{array}{llll}\text { i). } 2 \text { and } 3 & \text { (ii). } 19 \text { and } 19.01 & \text { (iii), } 4 \text { and }-2\end{array} \) \( \begin{array}{lll}\text { b). Prove that } 1+\sqrt{2} & \text { is irrational }\end{array} \)

Find a formula for the general term \( a_{n} \) of the sequence assuming the pattern of the first few terms continues. \[ \{2,-1,-4,-7,-10, \ldots\} \] Assume the first term is \( a_{1} \). \( a_{n}=\square \) Next Question

Below is the graph of \( y=\log _{4} x \) Translate it to become the graph of \( y=\log _{4}(x+2)+3 \)