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determination of log table value
If you are using a scientific calculator you will have a key labelled "log". To find the logarithm (to base 10) of a number, simply enter "log" followed by the number that you want to log. If you want a natural logarithm - log to the base e - use the "ln" key instead. If you haven't got a scientific calculator, use the one on your computer.
Subtract the log of the divisor from the log of the dividend and then us the antilog table to find the value of the quotient.When using log tables:It is easiest to use logs to base 10;write the numbers in scientific notation, rounding to significant figures equal to the number of figures of the table;look up the mantissa (the bit before the × 10ⁿ) in the log table to get a value between 0 and 1;consider the exponent (the power of 10) as a number to be added to this log value;do the subtraction in two separate parts: subtract the whole numbers and subtract the fractional part (after the decimal point);if the fractional part is negative, add 1 to it to make it positive and subtract 1 from the whole number;look up the fractional part in the antilog table;multiply this value by 10 to the power of the whole number.Instead of rounding to the figures of the table, you can interpolate between the values in the table, but it is likely to not make much difference to the final value, which is only accurate to a maximum of the figures of the table.When adding the exponent to the looked up log value, if it is negative, write is as the absolute value with a bar over it. This is not a strictly correct use of the decimal point - it is really writing something like -1 + 0.345 in a compact form; the point is that the part after the decimal point is always positive whereas the whole number part is the part which may be negative.If you do not have antilog tables, you can find the antilog by finding the log value inside the table and finding the value in the headings.eg in my 3 figure tables, the log of 3.45 is looked up by finding where row 3.4 intercepts column 5 giving a value of 538 which is 0.538.To find the antilog of 0.307 I find 307 in row 2.0 under column 3 meaning the antilog of 0.307 is 2.03If the exact value does not appear in the table, you can interpolate between values to get the closest approximation. eg the antilog of 0.308: 307 → 2.03, 310 → 2.04; 308 is closest to 307, so the antilog to 3 figures would be 2.03Using 3 figure logs to base 10:3533 ÷ 9043 = (3.533 × 10³) ÷ (9.043 × 10³)= 10^(lg(3.533 × 10³) - lg(9.043 × 10³))≈ 10^(lg(3.53 × 10³) - lg(9.04 × 10³))≈ 10^((3 + 0.548) - (3 + 0.956))= 10^(0 - 0.408)= 10^((0 - 1) + (1 - 0.408))= 10^(-1 + 0.592)≈ 3.91 × 10⁻¹= 0.391(Using a calculator I get 3533 ÷ 9043 = 0.39068893..... which to 3 sig fig is 0.391 as found using the log table.)-------------------------------------------------A slide rule is an analogue log table.
first u must find x...then multiply it by 7 to get the angle...then look up the sin ratio of that angle in your log table
In order to find the log with a power of ten, use the LOG button. For example, to find log105, type log(5). (The parenthesis after the g will appear when you press the LOG button. In order to find a log with a power other than ten, you will have to divide by the log10 of that power. For example, to find log82, type log(8)/log(2). In order to find the natural log of a number, use the LN key. For example, to find the natural log of 91, type ln(91).