Evaluate each expression. \[ \begin{array}{l}\text { (a) } \log _{7} \frac{1}{7}=\square \\ \text { (b) } \log _{3} 27=\square\end{array} \]

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) \( 2 \log _{8} 5=\log _{8} \square \)

2 Beräkna a) \( 10^{3}-10^{2} \)

If \( x \) and \( y \) are the dimensions of a rectangle whose area is 8 and whose perimeter is as small as possible, then \( x^{2}+y^{2}= \) a. 32 b. 12 c. 20 d. 24 e. 16

Evaluate. \[ \frac{(-4-3)^{2}-10}{3-4^{2}} \]

If \( f(x)=6^{7-x}+1 \), what is the value of \( f(2) \), to the nearest ten-thousandth (if necessary)?