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This video tutorial demonstrates how to solve equations with an unknown as a power using logarithms. The equations provided have different variations, one with the power on one term and the other with the power on two terms. By using the definition of logarithms, where the logarithm of a number in a base equals x, we can find the value of the unknown. In the example shown with a base of 3, an unknown variable X can be determined as the logarithm of 12 in base 3.