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Math 116.05 - Midterm 2 Practice
(1) Consider the function
f (x) = log2 (6 − 2x).
(a) Find the domain and range of f (x).
(b) Find f −1 (x).
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(2) Solve these equations for x:
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(a) 2(x −2x) − 1 = 7
(b)
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log3 (2x + 1) = 3
Math 116.05
(3) (a) Rewrite the following as a sum of logarithms, using no products: log5 (3xy)
(b) Rewrite the following in terms of natural logarithm: log3 (x)
(c) Rewrite the following without exponents: log3 (x2 )
(d) What is the value of eln x ?
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(4) Which is worth more now, if we can get an effective annual interest rate of 5%?
• A lump sum of $2000 ten years from now.
• $1000 five years from now and $900 ten years from now.
• $1500 cash today.
Math 116.05
(5) Which will be worth more in five years?
• $1000 earning 4% interest, compounded continuously.
• $1100 earning 4.5% interest, compounded monthly?
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(6) Solve the system
3x + 2y − z = 2
2x + 2y − z = 10
−4x + y + 2z = 6
Math 116.05
(7) If the supply equation is
p
=2
q
and the demand equation is
p(3q + 1) = 3,
find the market equilibrium price and quantity.
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