Write the expression as a sum and/or difference of logarithms. Express powers as factors. \( \ln \left(x^{12} \sqrt{7-x}\right), 0<x<7 \) \( \ln \left(x^{12} \sqrt{7-x}\right)=\square \) (Simplify your answer.)

The retail flat rate in dollars for first-class mail weighing up to 5 ounces could be computed by the piecewise-constant function \( f \), where \( x \) is the number of ounces. (a) Evaluate \( f(1.1) \) and \( f(4) \). Interpret your results. (b) Sketch a graph of \( f \). What is the domain of \( f \) ? What is the range of \( f \) ?

Consider the following function. \[ f(x)=1-x^{2 / 3} \] Find \( f(-1) \) and \( f(1) \) \( f(-1)=\square \) \( f(1)=\square \)

Which of the following is equal to \( \log \sqrt[4]{1000} \) ? ( 1 point) \( \begin{array}{l}\frac{3}{4} \\ -\frac{4}{3} \\ -\frac{3}{4}\end{array} \)

What value is equivalent to \( \log _{2} 13 \) to the nearest thousandth? Use the change of base formula to determine your answer. (1 point) 0.270 3.700 0.813 0.557

Which of the following is the value of \( \log 10^{20} \) ? (1 point) \( \frac{1}{2} \) 2 200 20