Chapter 3
-------Section 4-------
Solving Exponential and
Logarithmic Functions
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Properties to use:
1. If ax = ay, then x = y. (a≠1).
2. If logax = logay, then x = y.
3. alogax = x.
4. logaax = x. (* logaax is the same as xlogaa).
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Example Problems:
a) 4x = 64
4x = 43
x = 3
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b) lnx – ln2 = 0
lnx = ln2
x = 2
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c) log4x – log6 = 0
log4x = log6
4x = 6
x = 3/2
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d) 10x = 7
log10x = log7
x = log 7
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e) lnx = 4
x = e4
x = 54.60
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f) 3(2x) = 42
(2x) = 14
Log2(2x) = log214
x = log214
x = log14/log2
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g) 2(32t-5) – 4 = 12
2(32t-5) = 16
32t-5 = 8
(2t-5)log3 = log8
2t – 5 = log8/log3
2t = log8/log3 + 5
t = 1/2(log8/log3 + 5)
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h) e2x – 3ex + 2 = 0
(ex – 2)(ex – 1) = 0
ex – 2 = 0 ex – 1 = 0
ex = 2 ex = 1
ln ex = ln2 ln ex = ln1
x = ln2 x = ln1
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i) ln(x – 2) + ln(2x – 3) = 2lnx
ln(x – 2)(2x – 3) = lnx2
(x – 2)(2x – 3) = x2
2x2 – 7x + 6 = x2
x2 – 7x + 6 = 0
(x – 6)(x – 1) = 0
x = 6 x = 1
(* x = 1 is an extraneous solution!)
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Remember...
* When the exponent is a variable:
1) Try to make the bases the same on both sides.
2) Take the log of both sides.
* If log = ___ , use exponential form. (f(x) = ax)
* Check for extraneous solutions! You cannot take the log of a negative number!
Comments (1)
Anonymous said
at 8:34 pm on Jan 8, 2008
Clean up the code in the table (but the table is a great addition to your page!). 19/20
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