Download 11.5 Common Logarithms

Pre-calc w-up 4/10-11
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Write the equation loge 13.7 = x in
exponential form
Write the equation (1/4)-4 = 256 in log
form
Evaluate the expression log443
Solve log2x + log210 = log270
11.5 Common Logarithms
A common logarithm is a
logarithm with a base of 10.
 log10x = logx
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Use your properties of logarithms to simplify.
Remember a logarithm is an exponent.
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Ex 1: Given log8 = 0.9031 evaluate
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A) log 800,000
= log (100,000 x 8)
= log 105 + log 8
= 5 + 0.9031
= 5.9031
The antilog…
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The inverse of a logarithm is a _______
exponent
So if log x = a then ________
10a = x
What…
1.06069784 – push the buttons on your calc
Log 11.5=_________
11.5 on calc push
Antilog 1.06069784 = _____________
2nd log 10^1.06069784
(inverse of log)
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Try these
 Answers
2a) log 54.1
1.7332
2b) antilog1.9484
88.7973
Change of base – we want base 10
then we can use our calculators.
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a,b,n are positive and a and b don’t equal
1 then the change of base formula is…
log b n
log a n 
log b a
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Ex 3: find the value of log9 1043
log1043
 use your calc  3.16
log 9
Use logs to solve exponential
functions..
Ex4: solve 63x = 81
 Take the log of both sides
 log63x = log 81
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“finding answers in the hunt powers of log can go up front”
3x log 6 = log 81 (now solve)
 3x = log81/log6
(divided both sides by log6)
 x = .8175 (divided both sides by 3)
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Ex 5: 12x-4 = 3x-2
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Take the log of both sides, bring powers up front
 (x – 4)log12 = (x – 2) log3
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You can NOT distribute the log, a log is an exponent
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Do you do this (x + 5)2 = x2 + 25
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Divide by a log 1st, (doesn’t matter which one) then
follow rules of solving.
NO
log 3
x  4  ( x  2)
now distribute
log12
x  4  ( x  2).4421
x  4  .4421x  .8842
x = 5.58 
Ex6: graph y= 3log(x+1)
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What is the basic shape of a logarithm?
Type it into your calc y = logx
 How does that compare to y = 10^x?
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Plug into your calculator, adjust window,
label at least 3 points.
Remember:
Logs in real number system are
undefined for negative numbers.
 You can get a negative answer, you can’t
take a log of a negative number
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Homework: pg 730 # 19-21,23,28 – 45 all
19-23 NO CALC
 28-rest you can use a calculator
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