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The video demonstrates how to rewrite logarithm expressions in exponential form without using logs. The key to success in this form of question is understanding the rules of logarithms. The power rule states that a number in front of a log being multiplied to the log can be placed as a power of the base. The product rule states that when adding logs of the same base, you can multiply them. By applying these rules, the expression log A ^ 2 - b ^ 2 + 2 log a is rewritten as log A ^ 2 = log a - b + log b ^ 3.