Log, ln and Mathematical Operations

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Presentation transcript:

Log, ln and Mathematical Operations

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 0.001 = 1 x 10-3 = -3 Ex. Log 1 = 0

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 31.25 = 1.4949 (4 SF) (5 SF)

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

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

Sample Exercises [1.] Solve for x: a. Log 1,000,000 = x b. Log 78.90 = x c. Log 328.45 = x [2.] Solve for x: a. log x = 1.31 b. 1048.1 = x c. 103.68 = x

Natural log or Base e logarithm, ln the power to which e is raised to equal a certain number e has a value 2.71828 Example: e2.303 = 10 or 2.71828(2.303) = 10 Therefore: ln 10 = 2.303

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

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-5.156 = x c. ex = 12.1

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

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

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)