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SIGNIFICANT FIGURES WITH LOGARITHMS

 

BASE 10 LOGARITHMS
Terminology: If log(x) = y   then   x = inverse log of y   or   x = antilog(y)   or   x = 10y
Calculator: The inverse log button on your calculator is probably the same as the log button with the 2nd function button
SF Rule: The number of significant figures (SF) in x is the same as the number of decimal places (dp) in y
Examples - Find y:
x # of sf in x # of dp in y y = log(x)
3.4x108 2 2 8.53
0.00576 3 3 -2.240
2198.47 6 6 3.342121
5.93x10-4 3 3 -3.227
Examples - Find x:
y # of dp in y # of sf in x x = 10y
1.98 2 2 95
-6.243 3 3 5.71x10-7
7.5 1 1 3x107

NATURAL LOGARITHMS
Terminology: If ln(x) = y   then   x = inverse ln of y   or   x = antiln(y)   or   x = ey
Calculator: The inverse ln button on your calculator is probably the same as the ln button with the 2nd function button
SF Rule: The number of significant figures (SF) in x is the same as the number of decimal places (dp) in y
Examples - Find y:
x # of sf in x # of dp in y y = ln(x)
82.6 3 3 4.414
1.7x10-4 2 2 -8.68
0.03349 4 4 -3.3965
6x102 1 1 6.4
Examples - Find x:
y # of dp in y # of sf in x x = ey
12.6 1 1 3x105
7.398 3 3 1.63x103
-4.55 2 2 0.011 or 1.1x10-2

last modified 3 September 2011