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Section 4 - Solving Exponential and Logarithmic Equations

Page history last edited by PBworks 16 years, 3 months ago

 

 

 

Chapter 3

 

-------Section 4-------

 

Solving Exponential and

 

Logarithmic Functions

 

 

 

----------------------------------------------------

 

 

Properties to use:

 

1. If ax = ay, then x = y. (a1).

 

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

b)      lnx – ln2 = 0

 lnx = ln2

 x = 2

c)      log4x – log6 = 0

 log4x = log6

 4x = 6

 x = 3/2

 

d)     10x = 7

log10x = log7

x = log 7

e)      lnx = 4

x = e4

x = 54.60

f)       3(2x) = 42

(2x) = 14

Log2(2x) = log214

x = log214

      x = log14/log2

 

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)

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

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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