/*! 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 754 Express the logarithm of 7 to th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 26: Problem 754

Express the logarithm of 7 to the base 3 in terms of common logarithms.

Short Answer

Expert verified
The logarithm of 7 to the base 3 in terms of common logarithms is \(\log_3 7 = \frac{\log 7}{\log 3}\).

Step by step solution

01

Identify the given logarithm and the desired base

We are given the logarithm \(\log_3 7\) and we want to express it in terms of common logarithms, which are base 10.
02

Apply the change of base formula

Now we will use the change of base formula to convert our given logarithm to base 10. \(\log_{a}b = \frac{\log_{c}b}{\log_{c}a}\) In our case, \(a = 3\), \(b = 7\), and \(c = 10\). So, we have: \(\log_3 7 = \frac{\log_{10} 7}{\log_{10} 3}\)
03

Simplify the expression

We can now use the simplified notation for common logarithms, which is \(\log b = \log_{10} b\). So our expression becomes: \(\log_3 7 = \frac{\log 7}{\log 3}\)
04

Write the final answer

Now we have expressed the logarithm of 7 to the base 3 in terms of common logarithms: \(\log_3 7 = \frac{\log 7}{\log 3}\)

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

Find log \(2.563\)

Find the value of \(\mathrm{N}\) if \(\log _{8} \mathrm{~N}=2 / 3\).

Determine \(\mathrm{x}\) when \(\log \mathrm{x}=3.1818\).

Find \(\log _{9}(1 / 27)\)

Calculate \(50.73 / 2.42\), using logs and antilogs.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.