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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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