/*! 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 18 Write each equation in its equiv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 18

Write each equation in its equivalent logarithmic form. $$b^{3}=343$$

Short Answer

Expert verified
The equivalent logarithmic form of the equation \( b^{3} = 343 \) is \( \log_b 343 = 3 \)

Step by step solution

01

Understand the exponential form

We first look at the given equation which is in exponential form, \( b^3 = 343 \). Here, 'b' is the base, '3' is the exponent, and '343' is the result.
02

Applying the logarithmic conversion rule

According the rule of conversion from exponential form to logarithmic form, if \( b^3 = 343 \) , then its equivalent in logarithmic form would be \( \log_b 343 = 3 \). It simply expresses the operation which is 'b raised to what power results in 343'.

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

Complete the table for a savings account subject to contimuous compounding ( \(A=P e^{n}\) ). Round answers to one decimal place. Amount Invested 8000 dollar Annual Interest Rate 20.3% Accumulated Amount 12,000 dollar Time \(t\) in Years _______

This group exercise involves exploring the way we grow. Group members should create a graph for the function that models the percentage of adult height attained by a boy who is \(x\) years old, \(f(x)=29+48.8 \log (x+1) .\) Let \(x=5,6\) \(7, \ldots, 15,\) find function values, and connect the resulting points with a smooth curve. Then create a graph for the function that models the percentage of adult height attained by a girl who is \(x\) years old, \(g(x)=62+35 \log (x-4)\) Let \(x=5,6,7, \ldots, 15,\) find function values, and connect the resulting points with a smooth curve. Group members should then discuss similarities and differences in the growth patterns for boys and girls based on the graphs.

One problem with all exponential growth models is that nothing can grow exponentially forever. Describe factors that might limit the size of a population.

Use the exponential growth model, \(A=A_{0} e^{k_{i}},\) to show that the time it takes a population to triple (to grow from \(A_{0}\) to \(\left.3 A_{0}\right)\) is given by \(t=\frac{\ln 3}{k}\)

Use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution=set. Verify this value by direct substitution into the equation. $$5^{x}=3 x+4$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

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.