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# How to Expand Logarithms?

TopLogarithmic expressions can be used for linear representation of exponential data. These expressions are also often found to be compressed in order to avoid multiple recurrences of Logarithm function in a single expression. To make operations like Integration to be solved easily, these expressions are needed to be expanded. This is because expanding them leads to reduced and simpler expressions to be operated upon instead of complex ones including rational and exponential variants. Let’s proceed further to know how to expand logarithms. There are many simple Logarithm rules to be followed to expand them into their uncompressed forms.
Taking logarithm of an expression can be represented in general as:
x = yh,
Or log y x = h,
Where, 'h' is the power to which the number or the base 'y' has been raised to give 'x'. Although we can calculate logarithms by using several bases, still calculations become easy by considering base 10. There is one more fact to be remembered, if 'N' i.e. our number whose log is to be evaluated lies between 1 and 10 (1 < N < 10), its log value lies between 0 and 1 (0<log x<1).
If your expression consists of several multiplications, then this logarithmic expression can be expanded as the sum of the logs of individual quantities in multiplication. Their sum would result in same value. Say, we have expression log (x * y * z * l * m * n * o).
This expression can be written as log (x) + log (y) + log (z) + log (l) + log (m) + log (n) + log (o)
Similarly, in case expression you have includes the division operation. These types of expressions can be solved by taking log of individual quantities and subtracting them. Say, we have expression as log (d / e). This expression can be written as log (d) – log (e).
In this way we can expand all logarithmic expressions.