Write the equation in its equivalent logarithmic form.  b3=2744{“version”:”1.1″,”math”:”b3=2744″}

Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.  log1263.2{“version”:”1.1″,”math”:”log1263.2″}

Write the equation in its equivalent exponential form.  logb64=3{“version”:”1.1″,”math”:”logb64=3″}

Evaluate the piecewise function at the given value of the independent variable.  h(x) =x2-7x+6if x ≠-6x -2if x =-6; h (-6){“version”:”1.1″,”math”:”h(x) =x2-7x+6if x ≠-6x -2if x =-6; h (-6)”}

Use the center, vertices, and asymptotes to graph the hyperbola.  (y+2)29-(x-1)216=1{“version”:”1.1″,”math”:”(y+2)29-(x-1)216=1″}

Evaluate the expression without using a calculator.  log214{“version”:”1.1″,”math”:”log214″}

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.  3x+54-2x≥0{“version”:”1.1″,”math”:”3x+54-2x≥0″}

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.  log2(x+4) – log2(x-2) =2{“version”:”1.1″,”math”:”log2(x+4) - log2(x-2) =2″}

[All solutions must start by writing an equation (or equations) from the equation sheet on your paper.  The solution must then follow a logical progression from the equation(s) on the equation sheet to the answer(s).] You, ever the adventurer, are taking a hot air balloon on a trip. It begins by moving straight upwards at a constant rate of 14 m/s. When it reaches an altitude of 100 meters, you drop a weight off of the edge of the moving balloon. How many seconds will pass before the weight hits the ground? What will the magnitude of the velocity vector be when it reaches the Earth?

For this question, use up as the positive y-direction.  A ball is thrown upward.  Before the ball reaches its peak and begins to head downward…