MATH 1090 - SUMMER 2007 - ASSIGNMENT #6
Exponential and Logarithmic Functions
(1) Evaluate the functions f(x) = 2xand g(x) = (1
2)xat the points
x=−4,−3,−2,−1,0,1,2,3,4
and draw their graphs. Warning: the graphs of gand fare very different.
(2) Without using a calculator, just the rules for exponents (page 177 in book) calculate
the following: 4 3
2,0.1252
3,1.50,3−1.
(3) Find the compounded amount and the interest in the following cases:
(a) principal = $1000, after one year, at APR=6% compounded annually.
(b) principal = $1000, after 5 years, at APR=6% compounded annually.
(c) principal = $1000, after one year, at APR=6% compounded quarterly.
(d) principal = $1000, after 5 years, at at APR=6% compounded quarterly.
(4) Without a calculator, using the rules for logarithms calculate:
log2(2) ,log2(1) ,log1.44 (1) ,log2¡1
2¢
log3.5¡1
3.5¢,log2¡1
4¢,log2(32) ,log10 (0.0001)
(5) Using the rules for logarithms simplify the following expressions so that they contain
only log2(3) and log2(5): log2¡4
√3¢,log2(15) ,log2(9) ,log2¡1
3¢,log2¡5
3¢,log3(5)
(6) Use the conversion formula to calculate the following expressions using the log button
in your calculator: log1.04(1.87),log1.1(0.9),log37,log 9
2(3
4)
(7) Simplify the following expressions, write them in terms of log(x),log(x+1),log(x+2):
(a) log h¡x
x+1 ¢3i
(b) log h√x
(x+1)2(x+2)3i
(8) Do the opposite of what you did in 7 to combine these expressions into a single
logarithm:
(a) log5(x+ 3) −log5(x−15)
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