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 77d
Capitolo 1, Problema 77d

Determine whether the following statements are true and give an explanation or counterexample.


2=10log1022=10^{\(\log\)_{10}2}

Guida verificata passo dopo passo
1
Step 1: Understand the statement. The statement given is 2 = 10^{\(\log\)_{10}2}.
Step 2: Recall the property of logarithms. One important property is that if a = b^{\(\log\)_b(a)}, then the statement is true.
Step 3: Apply the property to the given statement. Here, a = 2 and b = 10, so we have 2 = 10^{\(\log\)_{10}(2)}.
Step 4: Verify the property. Since the base of the logarithm (10) and the base of the exponent (10) are the same, the property holds true.
Step 5: Conclude that the statement is true based on the logarithmic property.

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:
1m

Concetti chiave

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

Logarithmic Identity

The logarithmic identity states that for any positive number 'a' and 'b', the equation a = b^log_b(a) holds true. This means that raising the base 'b' to the logarithm of 'a' with base 'b' will yield 'a'. This identity is fundamental in understanding how logarithms relate to exponentiation and is crucial for evaluating expressions involving logarithms.
Video consigliato:
7:17
Verifying Trig Equations as Identities

Properties of Logarithms

Logarithms have several key properties that simplify calculations, such as the product, quotient, and power rules. For instance, log_b(xy) = log_b(x) + log_b(y) and log_b(x/y) = log_b(x) - log_b(y). Understanding these properties allows for the manipulation of logarithmic expressions, which is essential for verifying the truth of statements involving logarithms.
Video consigliato:
05:36
Change of Base Property

Base of a Logarithm

The base of a logarithm is the number that is raised to a power to obtain a given number. In the expression log_b(a), 'b' is the base. Different bases can yield different results, and it is important to recognize that the base must be positive and not equal to one. This concept is critical when evaluating logarithmic expressions and understanding their implications in equations.
Video consigliato:
05:36
Change of Base Property
Pratica correlata
Domanda del libro di testo

Determine whether the following statements are true and give an explanation or counterexample.


2=ln2e2=\(\ln\)2^{e}

227
views
Domanda del libro di testo

Determine whether the following statements are true and give an explanation or counterexample.

log546=4log56\(\log\)_54^6=4\(\log\)_56

206
views
Domanda del libro di testo

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.


If f(x)=1xf\(\left\)(x\(\right\))=\(\frac{1}{x}\) , then f−1(x)=1xf^{-1}\(\left\)(x\(\right\))=\(\frac{1}{x}\)

245
views
Domanda del libro di testo

Determine whether the following statements are true and give an explanation or counterexample.


logbxlogby=logbx−logby\(\frac{\log_{b}\)x}{\(\log\)_{b}y}=\(\log\)_{b}x-\(\log\)_{b}y

217
views
Domanda del libro di testo

In each exercise, a function and an interval of its independent variable are given. The endpoints of the interval are associated with points PP and QQ on the graph of the function.

a. Sketch a graph of the function and the secant line through PP and QQ.

b. Find the slope of the secant line in part (a), and interpret your answer in terms of an average rate of change over the interval. Include units in your answer.

After tt seconds, an object dropped from rest falls a distance d=16t2d=16t^2, where dd is measured in feet and 2≤t≤52\(\leq{t}\)\(\leq{5}\).

486
views
Domanda del libro di testo

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.


If f(x)=x2+1f\(\left\)(x\(\right\))=x^2+1 , then f−1(x)=1x2+1f^{-1}\(\left\)(x\(\right\))=\(\frac{1}{x^2+1}\).

276
views