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 18
Capitolo 5, Problema 18

In Exercises 16–18, write each equation in its equivalent logarithmic form. 13^y = 874

Guida verificata passo dopo passo
1
Identify the general relationship between exponential and logarithmic forms. The exponential form is written as a^b = c, and its equivalent logarithmic form is log_a(c) = b.
Compare the given equation 13^y = 874 with the general exponential form a^b = c. Here, the base (a) is 13, the exponent (b) is y, and the result (c) is 874.
Rewrite the equation in logarithmic form using the relationship log_a(c) = b. Substitute the base (13), the result (874), and the exponent (y) into the logarithmic form.
The equivalent logarithmic form of the equation is log_13(874) = y.
This means that y is the power to which 13 must be raised to produce 874.

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.

Exponential Equations

Exponential equations are mathematical expressions where a variable appears in the exponent. In the equation 13^y = 874, 13 is the base, y is the exponent, and 874 is the result of the exponentiation. Understanding how to manipulate these equations is crucial for converting them into logarithmic form.
Video consigliato:
5:47
Solving Exponential Equations Using Logs

Logarithmic Form

Logarithmic form is a way to express exponential equations using logarithms. The equation a^b = c can be rewritten as log_a(c) = b, where 'a' is the base, 'c' is the result, and 'b' is the exponent. This transformation is essential for solving equations involving exponents and understanding their properties.
Video consigliato:
7:30
Logarithms Introduction

Properties of Logarithms

Properties of logarithms include rules that simplify the manipulation of logarithmic expressions, such as the product, quotient, and power rules. These properties help in solving logarithmic equations and understanding their behavior. Familiarity with these rules is important when converting exponential equations to logarithmic form.
Video consigliato:
5:36
Change of Base Property
Pratica correlata
Domanda del libro di testo

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = (0.6)x

944
views
Domanda del libro di testo

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options:

f(x)=3x,g(x)=3x−1,h(x)=3x−1,f(x)=−3x,G(x)=3−x,H(x)=−3−x.f(x) = 3^x, \(\quad\) g(x) = 3^{x-1}, \(\quad\) h(x) = 3^x - 1, \\ f(x) = -3^x, \(\quad\) G(x) = 3^{-x}, \(\quad\) H(x) = -3^{-x}.

1688
views
Domanda del libro di testo

Write each equation in its equivalent logarithmic form. b3 = 1000

1011
views
Domanda del libro di testo

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 4x=1/√2

776
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. lnx5\(\ln\)\(\sqrt\)[5]{x}

876
views
Domanda del libro di testo

Write each equation in its equivalent logarithmic form. 7y = 200

777
views