Question

Problems $65-68$ are based on material earned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Write as a single logarithm: $\log _{7} x+3 \log _{7} y-\log _{7}(x+y)$

Name: Problem 66, Chapter 9: Algebra and Trigonometry
Uploaded: 2020-06-23T20:37:14-08:00
Duration: 2 min 27 s
Channel: Evan Leonard
Description: Problems 65-68 are based on material earned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Write as a single logarithm: log7 x+3 log7 y-log7(x+y)

   Problems $65-68$ are based on material earned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
Write as a single logarithm: $\log _{7} x+3 \log _{7} y-\log _{7}(x+y)$

Algebra and Trigonometry

Michael Sullivan 10th Edition

Chapter 9, Problem 66

Instant Answer

Solved by Expert Evan Leonard

06/23/2020

Step 1

The power rule states that $a \log_b c = \log_b c^a$. So, the expression becomes: \[ \log _{7} x+ \log _{7} y^{3} -\log _{7}(x+y) \] Show more…

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Problems $65-68$ are based on material earned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Write as a single logarithm: $\log _{7} x+3 \log _{7} y-\log _{7}(x+y)$

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Key Concepts

Power Rule for Logarithms

This rule allows us to move a coefficient in front of a logarithm to an exponent on the argument. It is key for simplifying expressions where constants multiply logarithms, transforming them into exponentials inside the logarithmic function.

Quotient Rule for Logarithms

This rule states that the difference between two logarithms with the same base is equal to the logarithm of the quotient of their arguments. It enables the consolidation of subtracted logarithmic expressions into a single logarithm through division.

Product Rule for Logarithms

This rule states that the sum of two logarithms with the same base is equal to the logarithm of the product of their arguments. It is essential for combining logarithmic expressions that are added together into one single logarithm.

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