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Stitz-Zeager_College_Algebra_e-book

# 2 naturally you withdraw your money and try to invest

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Unformatted text preview: ange of base formula to approximate the following logarithms. (a) log3 (12) (b) log5 (80) (c) log6 (72) 1 10 (e) log 3 (1000) (d) log4 5 (f) log 2 (50) 3 356 Exponential and Logarithmic Functions 5. Compare and contrast the graphs of y = ln(x2 ) and y = 2 ln(x). 6. Prove the Quotient Rule and Power Rule for Logarithms. 7. Give numerical examples to show that, in general, (a) logb (x + y ) = logb (x) + logb (y ) (b) logb (x − y ) = logb (x) − logb (y ) logb (x) x = (c) logb y logb (y ) 8. The Henderson-Hasselbalch Equation: Suppose HA represents a weak acid. Then we have a reversible chemical reaction HA H + + A− . The acid disassociation constant, Ka , is given by Kα = [H + ][A− ] [A− ] = [H + ] , [HA] [HA] where the square brackets denote the concentrations just as they did in Exercise 6c in Section 6.1. The symbol pKa is deﬁned similarly to pH in that pKa = − log(Ka ). Using the deﬁnition of pH from Exercise 6c and the properties of logarithms, derive the Henderson-Hasselbalch Equation which states [A− ] pH = pKa + log [HA] 9. Research the history of logarithms including the origin of the word ‘logar...
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