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Today, Vox Academy teaches how to add and subtract logarithms. Logarithms have a structure with a base to an exponent resulting in a number. Logarithms are expressed as log(base) = exponent, with a random number at the end. For example, 3 to the power of 2 equals 9, which can be expressed as log(base 3) = 2, where 9 is the number. Adding and subtracting logarithms involve combining like terms, such as log(base 3) = 27 + log(base 8) = 18 - log(base 16) = 4.