/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 Write as the sum or difference o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 20

Write as the sum or difference of logarithms and simplify, if possible. Assume all variables represent positive real numbers. $$\log _{7} \sqrt[3]{4}$$

Short Answer

Expert verified
The given expression can be rewritten as a sum or difference of logarithms by following these steps: 1. Rewrite the cube root using a fractional exponent: \(\log _{7} \left(4^{\frac{1}{3}}\right)\) 2. Apply the power rule of logarithm: \(\frac{1}{3} \log _{7} 4\) The simplified expression is: \(\frac{1}{3} \log _{7} 4\)

Step by step solution

01

Rewrite the cube root using a fractional exponent

To rewrite the given expression, we can first rewrite the cube root as a power of 4 by using a fractional exponent (Since the cube root of a number can be written as that number raised to the power of 1/3): \(\log _{7} \left(4^{\frac{1}{3}}\right)\)
02

Apply the power rule of logarithm

Now, we can use the power rule of logarithm, which states that \( \log_b(a^x) = x\log_b(a) \), to simplify the expression further: \(\frac{1}{3} \log _{7} 4\)
03

Simplify if possible

At this point, the expression cannot be simplified any further since it's already the sum or difference of logarithms. The final answer is: \(\frac{1}{3} \log _{7} 4\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve equation. \(\log _{6}(13-x)+\log _{6} x=2\)

The population of an Atlanta suburb is growing at a rate of 3.6\% per year. If 21,000 people lived in the suburb in 2004 , determine how many people will live in the town in \(2012 .\) Use \(y=y_{0} e^{0.036 t}\)

Determine whether each function is one-to-one. If it is one-to-one, find its inverse. $$g=\\{(0,-7),(1,-6),(4,-5),(25,-2)\\}$$

Write as a single logarithm. Assume the variables are defined so that the variable expressions are positive and so that the bases are positive real numbers not equal to \(1 .\) $$\frac{1}{3} \log _{a} 5-2 \log _{a} z$$

If \(f(x)=\sqrt[3]{x-10},\) show that \(f^{-1}(x)=x^{3}+10\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.