Solution of logarithms
To clarify the term logarithm of a number, it is easier to explain with an example. Mathematical expressions X = log515 and (5 to the power of X = 15) are identical. Hence, the logarithm of a number (X) is the exponent to which another number (the base of the power in our example «5») needs to be raised to obtain this number (15).
Expression (5 to the power of X = 15) is an exponential equation. Logarithms are used in complex calculations, and their use is characterized by the ability to replace such actions as multiplication with simpler addition. If numbers are replaced by their logarithms in calculations, the division operation can be replaced by subtraction.
Instead of extracting roots, one can perform division, and the operation of raising to a power can be replaced by multiplication. Among logarithms, decimal logarithms are most commonly used in practical calculations, lg (their base is the number «10») and natural logarithms ln (with the base of the number e = 2,718 ….).