1. Log, ln and Mathematical Operations

2. Log Known as common log or base-10 log
the power to which 10 is raised to equal a certain number
Ex. 103 = 1000; therefore log 1000 = 3
Ex. Log = 1 x 10-3 = -3
Ex. Log 1 = 0

3. Significant Figures
The number of digits after the decimal point equals the number of significant figures in the original number.
Ex. Log 23.5 = 1.371
3 sig. fig. = 3 sig. fig. After the decimal pt.
Ex. Log =
(4 SF) (5 SF)

4. Antilogarithms Is the reverse of taking a logarithm
For example, log 23.5 = 1.371
Therefore: antilog = 23.5
Is the process of raising 10 to a particular number to get that number (in this case, 23.5)

5. Use the following Calculator Keys:
10x or SHIFT log or INV log

6. Sample Exercises [1.] Solve for x: a. Log 1,000,000 = x
b. Log = x
c. Log = x
[2.] Solve for x:
a. log x = 1.31
b = x
c = x

7. Natural log or Base e logarithm, ln
the power to which e is raised to equal a certain number
e has a value
Example: e2.303 = or (2.303) = 10
Therefore: ln 10 = 2.303

8. Natural antilog Is the reverse of ln
Use the following Calculator Keys:
ex or INV ln

9. Sample Exercises [1.] Solve for x: a. ln 5.7 = x b. ln 321.8 = x
c. ln 7.9 = x
[2.] Solve for x:
a. ln x = 6.78
b. e = x
c. ex = 12.1

10. Correlation between log and ln
ln x = log x
ln (10) = log (10)
= (1)
ln and log are correlated by the factor 2.303

11. Mathematical Operations
Log xy = log x + log y
Log x/y = log x - log y
log an = n log a
log a 1/n = 1/n log a

12. Exercise Problems Solve the following: log 4 = log 0.000001 = ln 86
antilog of 77
natural antilog of 123
ln(600/740)
log (25 x 200)