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In this lesson, we focus on solving basic logarithmic equations. For example, log base 2 of 16 can be converted to 2 raised to the x equals 16, resulting in x equaling four. The change of base formula can also be used to find x. Another example is log base x of 81 equaling four, which can be rewritten as x to the fourth equals 81, making x equal to three. Similarly, log base five of x equals three becomes x equals five to the third, which simplifies to x equaling 125.