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**Unformatted text preview: **) x 2
3 3. (a) 7x−1 = e(x−1) ln(7)
log(x + 2)
(b) log3 (x + 2) =
log(3) (d) log(x2 + 1) = 4. (a) log3 (12) ≈ 2.26186 (d) log4 (b) log5 (80) ≈ 2.72271
(c) log6 (72) ≈ 2.38685 − 1 ln(z )
4 (c) 2 = ex ln( 3 )
ln(x2 + 1)
ln(10) 1
≈ −1.66096
10
(e) log 3 (1000) ≈ −13.52273
5 (f) log 2 (50) ≈ −9.64824
3 358 6.3 Exponential and Logarithmic Functions Exponential Equations and Inequalities In this section we will develop techniques for solving equations involving exponential functions.
Suppose, for instance, we wanted to solve the equation 2x = 128. After a moment’s calculation, we
ﬁnd 128 = 27 , so we have 2x = 27 . The one-to-one property of exponential functions, detailed in
Theorem 6.4, tells us that 2x = 27 if and only if x = 7. This means that not only is x = 7 a solution
to 2x = 27 , it is the only solution. Now suppose we change the problem ever so slightly to 2x = 129.
We could use one of the inverse properties of exponentials and logarithms listed in Theorem 6.3 to...

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