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Write an exponential form: t=log[99^s]
t=log[99^s] implies (99^s)=(e)^t if we are working out problems in calculus
t=log[99^s] implies (99^s)=(10)^t if we are working out numerical problems
Note: In problems of this variety the base has to be mentioned.
Otherwise the base when mentioned is taken to be the Naperian base e which is an irrational number more than 2 and less than 3. When e is the base the logarithm we are talking about is referred to as Natural logarithm. we consider natural logarithms while working out problems in calculus.
For numerical calculations if the base is not mentioned,it is taken to be 10 and the logarithm is referred to as common logarithm.
The definition of logarithm of a strictly positive number N to a given base b is defined as the power p to which the base has to be raised to give the number.
log(N) to the base b is = p implies and is implied by N=(b)^p