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Examples of logarithms:
log2 8 = 3 since 8 = 23
log10 0.01 = -2 since 0.01 = 10-2
log5 5 = 1 since 5 = 51
logb 1 = 0 since 1 = b
From the above illustration, it is evident that a logarithm is an exponent. 34 is called the exponential form of the number 81. In logarithmic form, 34 would be expressed as log 81 = 4, or the logarithm of 81 to the base 3 is 4. Note the symbol for taking the logarithm of the number 81 to a particular base 3, is log3 81, where the base is indicated by a small number written to the right and slightly below the symbol log.
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