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Rewriting exponential form to logarithm form and back. Solve logarithm equations.
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Day 3Common
Logarithms
Express each number using exponents.
OA. 36 G. 1OB. 121 What about . . .OC. 4 H. 345OD. I. 0.0023
OE. 100OF. 1000
Logarithms give you a way to solve for an exponent.
OEx: 5x = 12
Common Logarithms are any logarithm of base 10
Ex: log10 or log
Rewriting: 10b = a log10a=b
A. 102 = 100
B. 33 = 27
C. 25 = 32
log10 100 = 2
log3 27 = 3
log2 32 = 5
E. 641/2 = 8
F. log6 36 = 2
Log64 8 = 1/2
D. 9-2 = 1 81
G. log3 81 = 4
H. log14 = -2 1 196
I. log10 10 = 1
J. Log 1 = 0
Log9 = -2 1 81
62 = 36
34 = 81
101 = 10
100 = 1
14-2 = 1 196
Evaluate without a calculator:A. Log4 64
Step 1: set = to x Log4 64 = x
Step 2: rewrite in exp. form
4x = 64
Step 3: break down the #’s
22x = 26
Step 4: once the bases are the same, set exp. =
2x = 6
x = 3
B) Log5 125
5x = 125
5x = 55
x = 5
C) Log4 16
4x = 16
22x = 24
2x = 4
x = 2
D) Log343 7
343 = 7x
73x = 71
x = 1/3
Log343 7 = x
3x = 1
E) Log3
3x = 3-5
Log3 = x
x = -5
243 1
3x = 243 1
2431
Evaluate using a calculator.
A) Log 75 1.8751
B) Log -3 Not possible
** log10 (-3) = x
10x = -3
C) Log 1 0
** log10 1= x 10x = 1
But what if the base isn’t 10?Use Change of Base Formula:
logb a = or
A) log5 3 log 3log 5
= 0.6826
B) log11 18 log 18log 11
= 1.2054
C) log4 8 log 8log 4 = 1.5