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# Properties of Logarithms

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In this lesson, we will cover the properties of logarithms, including the product, quotient, and power rules. The product rule for logarithms allows us to simplify a logarithm of a product. The logarithm of a product is the sum of the logarithms of the factors. Similarly, the quotient rule for logarithms allows us to simplify a logarithm of a quotient. The logarithm of a quotient is the difference between the logarithm of the numerator and the logarithm of the denominator. The power rule for logarithms allows us to bring exponents outside the logarithm as coefficients. The logarithm of a number to a power is equal to the exponent multiplied by the logarithm of the number. These properties help us manipulate logarithmic expressions and condense or simplify when needed.

Properties of Logarithms:

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