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Unformatted text preview: n the solution has a pH of 12.2.
iii. [H+ ] = 10−0.7 ≈ .1995 moles per liter. 6.2 Properties of Logarithms 6.2 347 Properties of Logarithms In Section 6.1, we introduced the logarithmic functions as inverses of exponential functions and
discussed a few of their functional properties from that perspective. In this section, we explore
the algebraic properties of logarithms. Historically, these have played a huge rule in the scientiﬁc
development of our society since, among other things, they were used to develop analog computing
devices called slide rules which enabled scientists and engineers to perform accurate calculations
leading to such things as space travel and the moon landing. As we shall see shortly, logs inherit
analogs of all of the properties of exponents you learned in Elementary and Intermediate Algebra.
We ﬁrst extract two properties from Theorem 6.2 to remind us of the deﬁnition of a logarithm as
the inverse of an exponential function.
Theorem 6.3. (Inverse Propert...
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