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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.
When we take the logarithm of both sides of ELN(XY)=ELN(x)+LN(y), we obtain LN(ELN(XY))=LN(ELN(x)+LN(y)). The logarithms and exponential cancel each other out (equation (4)), giving our product rule for logarithms, LN(XY)=LN(x)+LN(y).
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.
The logarithm of x=1 is the number y we should raise the base b to get 1. Then the base 10 logarithms of 1 is 0.
log10 = ? If its base is 10 then log10 = 1. If its base is e then log10 = 2.3025. Log10 to the base 10 is 1.

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