Use properties to simplify logarithmic expressions

Translate between logarithms in any base Learning Targets Using the properties of exponents we can derive the properties of logarithms Properties of Logarithms Remember:

To multiply powers with the same base, you add the exponents. Product Property of Logarithms For any positive numbers m, n, and b,

The logarithm of a product is equal to the sum of the logarithms of its factors. Examples A B Remember:

To divide powers with the same base, you subtract the exponents. Quotient Property of Logarithms For any positive numbers m, n, and b,

The logarithm of a quotient is the logarithm of the dividend minus the logarithm of the divisor. Examples Because you can multiply logarithms, you can also take powers of logarithms. Power Property of Logarithms For any real number p and postive numbers a and b,

The logarithm of a power is the product of the exponent and the logarithm of the base. Examples Write as a single logarithm. Write as a single logarithm. Express as a product. Simplify. Remember:

Exponential and logarithmic operations undo each other so they are inverse operations. Inverse Property of Logarithms

and Exponents For any base b such that b>0 and b doesn't equal 1, Examples 1. 2. 3. The log button on your calculator is in base 10. We can change a logarithm with a different base to a logarithm in another base that we want. Change of Base Formula For a>0 and a not equal to 1 and any base b>0 and b not equal to 1, Examples 1. 2. 7.4 Properties of Logarithms

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# 7.4 Properties of Logarithms

Algebra 2B