/*! 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 123 Describe the following property ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 123

Describe the following property using words: \(\log _{b} b^{x}=x\).

Short Answer

Expert verified
The property \(\log _{b} b^{x}\) means that if a number is raised to an exponent, and then a log is taken with the same base as the number, the result is simply the exponent to which the number was initially raised.

Step by step solution

01

Identify the base and the exponent in the given property

In the given property \(\log _{b} b^{x}\), \(b\) is the base and \(x\) is the exponent.
02

Express the explanation of the property

This property means that when we take the logarithm of a number with the same base, the result is the exponent to which the base is raised. In other words, if a base \(b\) is raised to a power \(x\), then the log base \(b\) of \(b\) to the power \(x\) is \(x\). The log operation with the same base as the number essentially cancel each other out, leaving the exponent.
03

Provide an example for thorough understanding

For instance, for base 10, if we have \(10^2\), then \(\log_{10} 10^2 = 2\) which demonstrates the property \(\log _{b} b^{x}=x\). The log base 10 of 10 squared is 2 鈥� because 10 squared equals 100, and 10 needs to be multiplied by itself twice to get 100.

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 function \(P(t)=145 e^{-0.092 t}\) models a runner's pulse, \(P(t),\) in beats per minute, \(t\) minutes after a race, where \(0 \leq t \leq 15 .\) Graph the function using a graphing utility. TRACE along the graph and determine after how many minutes the runner's pulse will be 70 beats per minute. Round to the nearest tenth of a minute. Verify your observation algebraically.

Evaluate or simplify each expression without using a calculator. $$ e^{\ln 5 x^{2}} $$

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. $$ \log (x-15)+\log x=2 $$

Without using a calculator, determine which is the greater number: \(\log _{4} 60\) or \(\log _{3} 40\).

The percentage of adult height attained by a girl who is \(x\) years old can be modeled by $$f(x)=62+35 \log (x-4)$$ where \(x\) represents the girl's age (from 5 to 15 ) and \(f(x)\) represents the percentage of her adult height. Use the function to solve. Round answers to the nearest tenth of a percent. Approximately what percentage of her adult height has a girl attained at age \(13 ?\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Logic and Functions

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.