/*! 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 27 Evaluate the given quantities as... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 27

Evaluate the given quantities assuming that $$ \begin{array}{l} \log _{3} x=5.3 \text { and } \log _{3} y=2.1 \\ \log _{4} u=3.2 \text { and } \log _{4} v=1.3 \end{array} $$ $$ \log _{3}\left(x^{2} y^{3}\right) $$

Short Answer

Expert verified
We have the expression \(\log _{3}\left(x^{2} y^{3}\right)\). Using logarithm properties, we simplify this to \(2 \log _{3}(x) + 3 \log _{3}(y)\). Given \(\log _{3}(x)=5.3\) and \(\log _{3}(y)=2.1\), we substitute these values and evaluate the expression: \(2(5.3) + 3(2.1) = 10.6 + 6.3 = 16.9\). Therefore, \(\log _{3}\left(x^{2} y^{3}\right)=16.9\).

Step by step solution

01

Apply logarithm properties

The logarithmic expression given is \(\log _{3}\left(x^{2} y^{3}\right)\). We can make use of the logarithm properties to simplify this further. Recall that \(\log _{a}(bc)=\log _{a}(b)+\log _{a}(c)\), and \(\log _{a}(b^{n})=n\log _{a}(b)\). Applying these properties: \(\log _{3}\left(x^{2} y^{3}\right) = \log _{3}\left(x^2\right) + \log _{3}\left(y^{3}\right) = 2 \log _{3}(x) + 3 \log _{3}(y)\)
02

Substitute given values

Now we can substitute the given values for \(\log _{3} x\) and \(\log _{3} y\). \(\log _{3}(x)=5.3\) and \(\log _{3}(y)=2.1\) So we have: \(2 \log _{3}(x) + 3 \log _{3}(y) = 2(5.3) + 3(2.1)\)
03

Evaluate the expression

Now we can compute the value of the expression: \(2(5.3) + 3(2.1) = 10.6 + 6.3 = 16.9\) So \(\log _{3}\left(x^{2} y^{3}\right)=16.9\).

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

Suppose a savings account pays \(5 \%\) interest per year, compounded four times per year. If the savings account starts with \(\$ 600\), how many years would it take for the savings account to exceed \(\$ 1400 ?\)

Suppose \(y\) is such that \(\log _{2} y=17.67 .\) Evaluate \(\log _{2} y^{100}\)

Suppose \(x\) is such that \(\log _{6} x=23.41 .\) Evaluate \(\log _{6} x^{10}\).

The most intense recorded earthquake in Texas occurred in 1931 ; it had Richter magnitude \(5.8 .\) If an earthquake were to strike Texas next year that was three times more intense than the current record in Texas, what would its Richter magnitude be?

Show that if \(f\) is a function with exponential growth, then so is the square root of \(f\). More precisely, show that if \(f\) is a function with exponential growth, then so is the function \(g\) defined by \(g(x)=\sqrt{f(x)}\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

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.