Domanda del libro di testo
For a certain constant a>1, ln a≈3.8067 . Find approximate values of log₂ a and logₐ 2 using the fact that ln 2≈0.6931.
283
views
Ch. 1 - Functions
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 1.53
Solving equations Solve the following equations.
log₈ x = 1/3
Guida verificata passo dopo passo1
First, understand that the equation \( \log_8 x = \frac{1}{3} \) is asking for the value of \( x \) such that when 8 is raised to the power of \( \frac{1}{3} \), it equals \( x \).
Rewrite the logarithmic equation in its exponential form: \( x = 8^{\frac{1}{3}} \).
Recognize that raising a number to the power of \( \frac{1}{3} \) is equivalent to taking the cube root of that number.
Thus, \( x = \sqrt[3]{8} \).
Finally, simplify the expression \( \sqrt[3]{8} \) to find the value of \( x \).
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:
1mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Logarithms
Logarithms are the inverse operations of exponentiation, allowing us to solve for the exponent in equations of the form a^b = c. In the equation log₈ x = 1/3, it indicates that 8 raised to the power of 1/3 equals x. Understanding logarithmic properties is essential for manipulating and solving such equations.
Video consigliato:
7:30
Logarithms Introduction
Change of Base Formula
The Change of Base Formula allows us to convert logarithms from one base to another, which is particularly useful when dealing with bases that are not easily computable. The formula states that logₐ b = logₓ b / logₓ a for any positive x. This can simplify calculations, especially when using calculators that typically only compute base 10 or base e logarithms.
Video consigliato:
05:36Change of Base Property
Exponential Functions
Exponential functions are mathematical functions of the form f(x) = a^x, where a is a positive constant. They are crucial for understanding the relationship between logarithms and exponents. In the context of the given equation, recognizing that solving log₈ x = 1/3 involves rewriting it as an exponential equation helps in finding the value of x directly.
Video consigliato:
6:13Exponential Functions
Pratica correlata
Domanda del libro di testo
Missing piece Let g(x) = x² + 3 Find a function ƒ that produces the given composition.
(g o ƒ ) (x) = x⁴ + 3
285
views
Domanda del libro di testo
Simplify the difference quotient ƒ(x+h)-ƒ(x)/h
ƒ(x) = (x)/(x+1)
405
views
Domanda del libro di testo
Solving equations Solve the following equations.
7ˣ = 21
340
views
Domanda del libro di testo
Symmetry Determine whether the graphs of the following equations and functions are symmetric about the x-axis, the y-axis, or the origin. Check your work by graphing.
451
views
Domanda del libro di testo
Finding inverses Find the inverse function.
ƒ(x) = 3x² + 1, for x ≤ 0
358
views