Question

Express as an equivalent expression that is a sum or a difference of logarithms and, if possible, simplify. $$\log _{a} \frac{c-d}{\sqrt{c^{2}-d^{2}}}$$

Name: Problem 88, Chapter 12: Elementary and Intermediate Algebra
Uploaded: 2020-05-16T20:08:17-08:00
Duration: 2 min 34 s
Channel: Heather Zimmers
Description: Express as an equivalent expression that is a sum or a difference of logarithms and, if possible, simplify. loga (c-d)/(√(c^2-d^2))

   Express as an equivalent expression that is a sum or a difference of logarithms and, if possible, simplify.
$$\log _{a} \frac{c-d}{\sqrt{c^{2}-d^{2}}}$$

Elementary and Intermediate Algebra

Marvin L. Bittinger,… 4th Edition

Chapter 12, Problem 88

Instant Answer

Solved by Expert Heather Zimmers

05/16/2020

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Express as an equivalent expression that is a sum or a difference of logarithms and, if possible, simplify. $$\log _{a} \frac{c-d}{\sqrt{c^{2}-d^{2}}}$$

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Key Concepts

Logarithmic Properties

This concept involves using the rules of logarithms, such as the quotient rule (log(x/y) = log x - log y) and the power rule (log(x^r) = r log x). These rules allow us to break down complex logarithmic expressions into sums or differences that are easier to work with.

Radical Expressions and Fractional Exponents

This concept covers the technique of rewriting radicals as expressions with fractional exponents, for example, rewriting the square root of an expression as that expression raised to the 1/2 power. This conversion facilitates the application of logarithmic power rules to simplify expressions.

Difference of Squares

This algebraic identity states that a^2 - b^2 can be factored into (a - b)(a + b). Recognizing and applying this identity can help simplify expressions, especially when dealing with radicals that involve squared terms, enabling further reduction when used in conjunction with logarithmic properties.

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