Properties of Logarithms Apply, algebra homework help

1.REASONINGUse the properties of exponents to prove the Power Property of Logarithms. 2.Writing in Math Use the information given regarding exponents and logarithms on

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to explain how the properties of exponents and logarithms are related. Include examples like the one shown at the beginning of the lesson illustrating the Quotient Property and Power Property of Logarithms, and an explanation of the similarity between one property of exponents and its related property of logarithms in your answer.
GET READY for the Lesson
In Lesson 6-1, you learned that the product of powers is the sum of
their exponents.
9.81 = 32. 36 or 32 +4
In Lesson 9-2, you learned that logarithms are exponents, so you might
expect that a similar property applies to logarithms. Let’s consider a
specific case. Does log: (9.81) = log: 9 + log: 81? Investigate by
simplifying the expression on each side of the equation.
log: (9.81) = log2 (32 . 34) Replace 9 with 3² and 81 with 3*.
= 10g; 312 + 4)
Product of Powers
= 2 + 4 or 6
Inverse Property of Exponents and Logarithms
log: 9 + log: 81 = logz 32 + log3 34 Replace 9 with 3² and 81 with 3*,
= 2 + 4 or 6
Inverse Property of Exponents and Logarithms
Both expressions are equal to 6. So, log3 (9.81) = log3 9+ log3 81.