4.6 Solving Logarithm Problems 2011 May 02, 2011
4.6 Solving Logarithm Problems
Objective: Solve logarithmic or exponential equations using the properties of logs.
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4.6 Solving Logarithm Problems 2011 May 02, 2011
Solve by Eliminating Logs
log5(x2+5) = log5(54)
x2+5 = 54
x2 = 49
x = +­ 7
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4.6 Solving Logarithm Problems 2011 May 02, 2011
Solve by Eliminating Logs
1
/2log7(x) = 3log7(2)
log7(x1/2) = log7(23)
x1/2 = 23
x
=8
( x )2 = 8 2
x = 64
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4.6 Solving Logarithm Problems 2011 May 02, 2011
Solve by Eliminating Logs
2log8(x) + log8(2) = 1
log8(x)2 + log8(2) = 1
log8(2x2) = 1
2x2 = 81
x2 = 4
x = +­ 2
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4.6 Solving Logarithm Problems 2011 May 02, 2011
Solve by Eliminating Logs
3log4(x+3) + log4(2) = 2
log4(x+3)3 + log4(2) = 2
log4(2(x+3)3) = 2
2(x+3)3 = 42
2(x+3)3 = 16
(x+3)3 = 8
3
(x+3)3 =
3
8
(x+3) = 2
x = -1
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4.6 Solving Logarithm Problems 2011 May 02, 2011
Solve Using Logs
5x = 8.5
log 5x = log 8.5
x log 5 = log 8.5
x=
log 8.5
/
log 5
x = 1.3297
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4.6 Solving Logarithm Problems 2011 May 02, 2011
Solve Using Logs
0.4x-1 = 2.1-x
ln 0.4x-1 = ln 2.1-x
(x-1) ln 0.4 = -x ln 2.1
x ln 0.4 - ln 0.4 = -x ln 2.1
- ln 0.4 = -x ln 0.4 - x ln 2.1
- ln 0.4 = x(-ln 0.4 - ln 2.1)
- ln 0.4
/(-ln 0.4 - ln 2.1) = x
x = 5.255
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4.6 Solving Logarithm Problems 2011 May 02, 2011
Solve Using Logs
(3/4)x = 5x+4
x log (3/4) = (x+4) log 5
x log (3/4) = x log 5 + 4 log 5
x log (3/4) - x log 5 = 4 log 5
x (log (3/4) - log 5) = 4 log 5
x=
4 log 5
/(log (3/4) - log 5)
x = -3.393
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4.6 Solving Logarithm Problems 2011 May 02, 2011
The BEAST is here!
ln(x5(x2 - 2x +1)) - 2 ln (x-1) = 5 ln x + ln ( 4x - 51)
ln(x5(x2 - 2x +1)) - ln (x-1)2 = ln x5 + ln ( 4x - 51)
( )
ln (x5(x2 - 2x +1) = ln (x5 ( 4x - 51))
(x-1)2
x5(x2 - 2x +1) = x5 ( 4x - 51)
(x-1)2
x5(x - 1)2 = x5 ( 4x - 51)
(x-1)2
x5 = x5 ( 4x - 51)
1 = 4x - 51
52 = 4x
x = 13
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4.6 Solving Logarithm Problems 2011 May 02, 2011
Homework:
page 313
(5 ­ 15 odd, 21 ­ 37 odd, 66, 68)
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