/*! 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 52 Use the properties of logarithms... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 52

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $$\ln \sqrt[3]{t}$$

Short Answer

Expert verified
The expanded form of \( \ln \sqrt[3]{t} \) is \( 1/3 \cdot \ln t \).

Step by step solution

01

Rewrite the Cube Root

First, the cube root of t can be rewritten as a power of t. Thus, \( \sqrt[3]{t} \) can be rewritten as \( t^{1/3} \).
02

Apply the Power Rule of Logarithms

Next, apply the power rule to the logarithm. The power rule states that \( \log_b m^n = n \cdot \log_b m \). Therefore, \( \ln t^{1/3} \) can be expanded to \( 1/3 \cdot \ln t \).

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

The amount of time (in hours per week) a student utilizes a math-tutoring center roughly follows the normal distribution \(y=0.7979 e^{-(x-5.4)^{2} / 0.5},\) \(4 \leq x \leq 7,\) where \(x\) is the number of hours. (a) Use a graphing utility to graph the function. (b) From the graph in part (a), estimate the average number of hours per week a student uses the tutoring center.

he value \(V\) (in millions of dollars) of a famous painting can be modeled by \(V=10 e^{k t},\) where \(t\) represents the year, with \(t=0\) corresponding to 2000 . In 2008 , the same painting was sold for \(\$ 65\) million. Find the value of \(k,\) and use this value to predict the value of the painting in 2014 .

An exponential growth model has the form ________ and an exponential decay model has the form ________.

(a) solve for \(P\) and (b) solve for \(t\). $$A=P\left(1+\frac{r}{n}\right)^{n t}$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log _{2}(2 x-3)=\log _{2}(x+4)$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

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.