/*! 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 71 Let \(\log _{b} 2=A\) and \(\log... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 71

Let \(\log _{b} 2=A\) and \(\log _{b} 3=C .\) Write each expression in terms of \(A\) and \(C\). $$\log _{b} 8$$

Short Answer

Expert verified
Hence, the expression \(\log_b 8\) in terms of \(A\) and \(C\) is \(3A\).

Step by step solution

01

Expression for \(\log_b 2\)

From the given, we have \(\log_b 2 = A\). This represents the logarithmic relation for '2' in base 'b' as 'A'.
02

Expression for \(\log_b 8\)

We need to recall that \(8 = 2^3\). Hence, applying the logarithm on both sides, we get: \(\log_b 8 = \log_b (2^3)\). Using the property of logarithms, \(\log_b a^n = n \log_b a\), we have: \(\log_b 8 = 3 \log_b 2\).
03

Substitute \(\log_b 2\) as 'A'

In the previous step, we obtained the expression \(\log_b 8 = 3 \log_b 2\). We already know that \(\log_b 2 = A\). Substituting this, we get: \(\log_b 8 = 3A\).

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 formula \(A=22.9 e^{0.0183 t}\) models the population of Texas, \(A,\) in millions, \(t\) years after 2005 a. What was the population of Texas in \(2005 ?\) b. When will the population of Texas reach 27 million?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. An earthquake of magnitude 8 on the Richter scale is twice as intense as an earthquake of magnitude 4

Graph \(f\) and \(g\) in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of \(f\). $$f(x)=\ln x, g(x)=\ln (x+3)$$

a. Evaluate: \(\log _{2} 16\) b. Evaluate: \(\log _{2} 32-\log _{2} 2\) c. What can you conclude about $$\log _{2} 16, \text { or } \log _{2}\left(\frac{32}{2}\right) ?$$

Write as a single term that does not contain a logarithm: $$e^{\ln 8 x^{5}-\ln 2 x^{2}}$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Pure 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.