Logarithms and log tables
See that a logarithm is the power the base is raised to, build the log graph as the mirror image of the exponential graph, and use characteristic, mantissa and antilogarithm with a log table.
- UK: Year 12
- France: grade 12
- Germany: grade 10
- Iran: grade 11
- Afghanistan: grade 11
- Syria: grade 12
- Palestine: grade 10
- Ukraine: grade 11
- Russia: grade 10
Guide
log₂64 is read "log base 2 of 64". It asks: what power of 2 gives 64? Since 26 = 64, the answer is 6. A logarithm and a power are two sides of one fact.
The graph of y = log₂x is the reflection of y = 2x in the line y = x, because x and y swap: the point (3, 8) becomes (8, 3).
A common (base 10) logarithm splits into a whole part, the characteristic, and a decimal part, the mantissa. The mantissa comes from the table; the characteristic comes from the place of the decimal point: multiplying by 10 adds 1 to the logarithm. The antilogarithm goes the other way: from the logarithm back to the number itself.
Common slips: dividing the number by the base instead of finding the power; swapping x and y; forgetting the characteristic; writing the logarithm instead of the number.