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Basic Algebra


How do I solve an equation with 2 logarithms added on the left-hand side and only a number on the right-hand side? The process is shown using the example log4(x+4)+log4(x-8)=3.

Translating word phrases into algebraic expressions.

Jeff's Gas Station sells regular unleaded gasoline for a dollar per gallon and premium gasoline for $1.76 less than twice the amount of regular unleaded gasoline. What is the cost of 1 gallon of premium gasoline?

Solving equalities.

Solve the open sentence. If there are no solutions or if it is true for all real numbers then indicate so. x + 11 < -1 or -1/2x < -4

Modern algebra

(a) Let F = { (matrix with first row; a 0, second row is 0 a) : a is an element of R Show that F is a field and that F ~= R (b) Give the definition of a cyclic group Prove that every subgroup H of a cyclic group G =<a> is itself cyclic

Looking for the value of x.

If x times 5 gives the same result as x less than 5, what is the value of x? (A)5 (B)6 (C)4/5 (D)5/6 (E) -5/4

Bacterial growth word problem using logarithms.

The number of bacteria N in a culture is given by the model N=250e^kt, where t is the time in hours, with t=0, corresponding to the time when N=250. When t=10, there are 280 bacteria. How long does it take the population to double in size? To triple in size?