Fill in the missing values to make the equations true. (a) \( \log _{5} 3+\log _{5} 4=\log _{5} \square \) (b) \( \log _{8} 11-\log _{8} \square=\log _{8} \frac{11}{5} \) (c) \( 2 \log _{8} 5=\log _{8} \square \)

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

Consider the following piecewise-defined function. \[ f(x)=\left\{\begin{array}{ll}\frac{-5}{x+3} & \text { if } x<-3 \\ -9 & \text { if } x=-3 \\ -x^{2}+4 & \text { if } x>-3\end{array}\right. \] Step 1 of \( 3: \) Evaluate this function at \( x=-10 \). Write the exact answer. Do not round. If the answer is undefined, write Und as your answer. Answer \[ f(-10)= \]

Find the gradiut of the points \( (1,6) \) and \( (2,3) \)

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