/*! 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 84 Evaluate or simplify each expres... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 84

Evaluate or simplify each expression without using a calculator. $$\log 10^{8}$$

Short Answer

Expert verified
The simplification of the expression \( \log 10^{8} \) renders 8.

Step by step solution

01

Understanding the expression

The given expression is \( \log 10^{8} \). The base of the logarithm here is 10 (since there's no other number indicating the base, it's 10), and the argument of the logarithm is \(10^{8}\). The general rule for logs is that logb(b^a) = a.
02

Applying logarithmic property

By this general rule, we conclude that the expression \( \log 10^{8} = 8 \) because it follows the format of logb(b^a) = a, where b is the base 10, and a is the power 8 in this scenario.

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

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. $$\log _{3}(4 x-7)=2$$

The loudness level of a sound, \(D,\) in decibels, is given by the formula $$D=10 \log \left(10^{12} I\right)$$ where \(I\) is the intensity of the sound, in watts per meter \(^{2} .\) Decibel levels range from \(0,\) a barely audible sound, to \(160,\) a sound resulting in a ruptured eardrum. (Any exposure to sounds of I3 0 decibels or higher puts a person at immediate risk for hearing damage.) What is the decibel level of a normal conversation, \(3.2 \times 10^{-6}\) watt per meter \(^{2} ?\)

The logistic growth function $$ P(x)=\frac{90}{1+271 e^{-0.122 x}} $$ models the percentage, \(P(x),\) of Americans who are \(x\) years old with some coronary heart disease. Use the function to solve Exercises \(43-46\) At what age is the percentage of some coronary heart disease \(50 \% ?\)

Complete the table for a savings account subject to \(n\) compoundings yearly \(\left[A=P\left(1+\frac{r}{n}\right)^{m}\right]\). Round answers to one decimal place. Amount Invested 7250 dollar Number of Compounding Periods 12 Annual Interest Rate 6.5% A ccumulated Amount 15,000 dollar Time \(t\) in Years ________

We see from the calculator screen at the bottom of the previous page that a logistic growth model for world population, \(f(x),\) in billions, \(x\) years affer 1949 is $$ f(x)=\frac{12.57}{1+4.11 e^{-0.026 x}} $$ Use this function to solve Exercises \(38-42\) How well does the function model the data showing a world population of 6.1 billion for \(2000 ?\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

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.