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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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