Question

Problems 64-67 are based on material learned 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. Use properties of logarithms to write $\log _4 \frac{\sqrt{x}}{z^3}$ as a sum or difference of logarithms. Express powers as factors.

Name: Problem 67, Chapter 8: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-06-23T20:37:14-08:00
Duration: 2 min 27 s
Channel: Evan Leonard
Description: Problems 64-67 are based on material learned 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. Use properties of logarithms to write log4 (√(x))/(z^3) as a sum or difference of logarithms. Express powers as factors.

   Problems 64-67 are based on material learned 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.
Use properties of logarithms to write $\log _4 \frac{\sqrt{x}}{z^3}$ as a sum or difference of logarithms. Express powers as factors.

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 8, Problem 67

Instant Answer

Solved by Expert Evan Leonard

06/23/2020

Step 1

Step 1: Identify the expression you need to rewrite using properties of logarithms: \[ \log_4 \frac{\sqrt{x}}{z^3} \] Show more…

Show all steps

Thanks for your feedback!

Problems 64-67 are based on material learned 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. Use properties of logarithms to write $\log _4 \frac{\sqrt{x}}{z^3}$ as a sum or difference of logarithms. Express powers as factors.

Play audio

Feedback

Evan Leonard and 91 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Radical to Exponential Conversion

Radicals can be rewritten as expressions with fractional exponents; for example, the square root of a variable, ?x, can be expressed as x^(1/2). This conversion is critical when applying the logarithm power rule to expressions that involve roots.

Logarithm Power Rule

This rule allows exponents within a logarithmic argument to be brought out as coefficients, represented as log_b(M^p) = p * log_b(M). This is particularly useful for simplifying expressions and handling powers and radicals within logarithms.

Logarithm Quotient Rule

This rule states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator, symbolically: log_b(M/N) = log_b(M) - log_b(N). This is essential when breaking down a logarithmic expression involving division into simpler, additive components.

Please give Ace some feedback