Skip to main content
Ch. 1 - Functions
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBriggs 3rd EditionCh. 1 - FunctionsProblema 73
Capitolo 1, Problema 73

Changing bases Convert the following expressions to the indicated base.


ln∣x∣\(\ln\)\(\left\)|x\(\right\)| using base 5

Guida verificata passo dopo passo
1
insert step 1: Recall the change of base formula for logarithms, which is \( \log_b a = \frac{\log_k a}{\log_k b} \), where \( b \) is the new base and \( k \) is the current base.
insert step 2: Identify the current expression \( \ln|x| \), which is a natural logarithm with base \( e \).
insert step 3: Apply the change of base formula to convert \( \ln|x| \) to base 5: \( \log_5|x| = \frac{\ln|x|}{\ln 5} \).
insert step 4: Recognize that \( \ln|x| \) is the numerator and \( \ln 5 \) is the denominator in the change of base formula.
insert step 5: The expression \( \ln|x| \) in base 5 is \( \frac{\ln|x|}{\ln 5} \).

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.

Change of Base Formula

The Change of Base Formula allows us to convert logarithms from one base to another. It states that for any positive numbers a, b, and x (where a and b are not equal to 1), the logarithm can be expressed as log_b(x) = log_a(x) / log_a(b). This is essential for solving logarithmic expressions in different bases.
Video consigliato:
05:36
Change of Base Property

Natural Logarithm

The natural logarithm, denoted as ln, is the logarithm to the base e, where e is approximately 2.71828. It is commonly used in calculus and mathematical analysis due to its unique properties, such as the derivative of ln(x) being 1/x. Understanding natural logarithms is crucial when converting expressions involving ln to other bases.
Video consigliato:
05:18
Derivative of the Natural Logarithmic Function

Absolute Value in Logarithms

The absolute value in logarithmic expressions, such as ln|x|, indicates that the logarithm is defined for both positive and negative values of x, as long as x is not zero. This is important because logarithms are only defined for positive arguments, and the absolute value ensures that the input remains valid regardless of the sign of x.
Video consigliato:
Percorso guidato
05:03
Initial Value Problems
Pratica correlata
Domanda del libro di testo

Evaluating inverse trigonometric functions Without using a calculator, evaluate the following expressions.

tan−13\(\tan\)^{-1}\(\sqrt\)3

364
views
Domanda del libro di testo

Find a trigonometric function ff represented by the graph in the figure. <IMAGE>

288
views
Domanda del libro di testo

Prove the following identities.

secθ=1cosθ\(\sec\)\(\theta\)=\(\frac{1}{\cos\theta}\)

475
views
Domanda del libro di testo

Prove the following identities.

tanθ=sinθcosθ\(\tan\)\(\theta\)=\(\frac{\sin\theta}{\cos\theta}\)

389
views
Domanda del libro di testo

A GPS device tracks the elevation EE (in feet) of a hiker walking in the mountains. The elevation tt hours after beginning the hike is given in the figure. <IMAGE>

Repeat the procedure outlined in part (a) for the secant line that passes through points PP and QQ.

372
views
Domanda del libro di testo

A GPS device tracks the elevation EE (in feet) of a hiker walking in the mountains. The elevation tt hours after beginning the hike is given in the figure. <IMAGE>

Find the slope of the secant line that passes through points AA and BB. Interpret your answer as an average rate of change over the interval 1≤t≤31\(\leq{t}\)\(\leq{3}\).

492
views