Skip to main content
Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 4 - Exponential and Logarithmic FunctionsProblema 27
Capitolo 5, Problema 27

Evaluate each expression without using a calculator. log2 (1/8)

Guida verificata passo dopo passo
1
Recognize that the expression is \( \log_2 \left( \frac{1}{8} \right) \), which asks for the exponent to which 2 must be raised to get \( \frac{1}{8} \).
Rewrite \( \frac{1}{8} \) as a power of 2. Since \( 8 = 2^3 \), then \( \frac{1}{8} = 2^{-3} \).
Substitute this back into the logarithm: \( \log_2 \left( 2^{-3} \right) \).
Use the logarithmic identity \( \log_b (b^x) = x \) to simplify the expression to \( -3 \).
Conclude that \( \log_2 \left( \frac{1}{8} \right) = -3 \), meaning 2 raised to the power of -3 equals \( \frac{1}{8} \).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Logarithm Definition

A logarithm answers the question: to what exponent must the base be raised to produce a given number? For example, log base 2 of 8 asks, '2 raised to what power equals 8?' Understanding this definition is essential to evaluate logarithmic expressions.
Video consigliato:
7:30
Logarithms Introduction

Properties of Exponents and Logarithms

Logarithms and exponents are inverse operations. Knowing that 1/8 can be written as 2 to the power of -3 (since 8 = 2^3) allows rewriting the logarithm in terms of exponents, making it easier to evaluate without a calculator.
Video consigliato:
5:36
Change of Base Property

Evaluating Logarithms of Fractions

When evaluating logarithms of fractions, express the fraction as a power of the base with a negative exponent. For example, log2(1/8) becomes log2(2^-3), which simplifies to -3 by the logarithm definition.
Video consigliato:
5:14
Evaluate Logarithms
Pratica correlata
Domanda del libro di testo

Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 5x=17

704
views
Domanda del libro di testo

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb ((x2y)/z2)

1186
views
Domanda del libro di testo

Begin by graphing f(x) = 2x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2x – 1

884
views
Domanda del libro di testo

Evaluate each expression without using a calculator. log7 √7

826
views
Domanda del libro di testo

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log6 (36/(√(x+1))

861
views
Domanda del libro di testo

Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. ex=5.7

1547
views