You can convert to the same base, by the identity: logab = log b / log a (where the latter two logs are in any base, but both in the same base).
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The base of common logarithms is ten.
In math, that may either refer to changing the base of the number system (for example, change from decimal (base 10) to binary (base 2)); or it may refer to changing logarithms, from one base to another - for example, common (base-10) logarithms to natural (base-e) logarithms.
Because when the system of logarithms with the base 'e' was defined and tabulated, it was entitled with the identifying label of "Natural Logarithms". ---------------------------------- My improvement: The natural log base is e (a numerical constant of about 2.718). It is chosen as a log base since there is a mathematical series (a "string" of mathematical numerical terms to be summed) for calculating a logarithm (ie. exponent of the base) of a number, which has a base of e. Series for calculating logarithms with bases other than e have basically not been developed.
log 2 = 0.30102999566398119521373889472449 for base 10 logarithms
Besides using a calculator, there are tables of logarithms. You can find the antilog that way. See the related link.