Stitz-Zeager_College_Algebra_e-book

# 64 logarithmic equations and inequalities 642 377

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Unformatted text preview: feel so strongly about showing students that every property of logarithms comes from and corresponds to a property of exponents that we have broken tradition with the vast majority of other authors in this ﬁeld. This isn’t the ﬁrst time this happened, and it certainly won’t be the last. 354 Exponential and Logarithmic Functions 3. Applying the change of base with a = 4 and b = e leads us to write log4 (5) = ln(5) ln(4) . Evaluating ln(5) ln(4) this in the calculator gives ≈ 1.16. How do we check this really is the value of log4 (5)? By deﬁnition, log4 (5) is the exponent we put on 4 to get 5. The calculator conﬁrms this.4 ) 4. We write ln(x) = loge (x) = log(x) . We graph both f (x) = ln(x) and g (x) = log(e both graphs appear to be identical. log(x) log(e) y = f (x) = ln(x) and y = g (x) = 4 Which means if it is lying to us about the ﬁrst answer it gave us, at least it is being consistent. and ﬁnd log(x) log(e) 6.2 Properties of Logarithms 6.2.1 355 Exercises 1. Expand the following using the properties of logarithms and simplify. Assume when necessary that all quant...
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## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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