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Definition. The logarithm is denoted “logo x” (pronounced as “the logarithm of x to base b” or “the base-b logarithm of x” or (most commonly) “the log, base b, of x”). In the equation y = logo x, the value y is the answer to the question “To what power must b be raised, in order to yield x?”.
The logarithm of the ratio of two quantities is the logarithm of the numerator minus the logarithm of the denominator. Rule 3: Power Rule. The logarithm of an exponential number is the exponent times the logarithm of the base. Rule 4: Zero Rule. The logarithm of 1 such that b > 0 b > 0 b>0 but b1 equals zero.
In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient. This calculation is applicable in engineering problems involving heat and mass transfer.
log 100 = 2. Because. 102 = 100. This is an example of a base-ten logarithm. Log2 8 = 3. Because. 23 = 8. In general, you write log followed by the base number as a subscript. Log. Log a = r. LN. LN a = r.
Calculating logarithm of an expression with a base 1 is pointless. Log of a number is the power to which the base should be raised to get the number. The expression says (a) raised to the power x gives N. So if you take the base as 1, 1 raised to the power of anything would give you 1.
So 0, 1, and every negative number presents a potential problem as the base of a power function. And if those numbers can't reliably be the base of a power function, then they also can't reliably be the base of a logarithm. For that reason, we only allow positive numbers other than 1 as the base of the logarithm.
The value of log 1 base 1 is 0 and son it is said to be undetermined.
Why log(0) is not defined. The real logarithmic function logo(x) is defined only for x>0. So the base b logarithm of zero is not defined.
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