Using known properties of logarithms, one can expand a complex logarithmic expression into a series of simpler expressions. Logarithmic expressions are abbreviated with log and may involve combinations of multiplication, division and exponents.
Logarithmic expressions that contain multiplied terms are expanded by splitting the expression into the logarithms for each individual term added together. For instance, the log of a times b equals the log of a plus the log of b. When terms in a logarithmic expression are divided, expanding the expression requires subtracting the logs of the terms. The log of a divided by b equals the log of a minus the log of b. Finally, the logarithm of a number raised to an exponent equals the exponent times the log of the original number. Many logarithmic expressions involve combinations of terms, and a series of steps is needed for proper expansion.