Rewrite each expression as a single logarithm. Then evaluate the expression without a calculator.
1.) log 5 + log 20
2.) log 3 – log 30
3.) 2 log 400 – log 16
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Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Aplot of land has been surveyed for a new housing development with borders ab, bc, dc, and da. the plot of land is a right trapezoid with a height of 60 feet and an opposite leg length of 65 feet

The equation |pl = 2 represents the total number of points that can be earned or lost during one turn of a game. which best describes how many points can be earned or lost during one turn? o o -2 2 oor 2 -2 or 2 o