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 55
Capitolo 5, Problema 55

In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 11. log3−3logx\(\log\)3-3\(\log\) x

Guida verificata passo dopo passo
1
Identify the given expression: \(\log 3 - 3 \log x\).
Recall the logarithmic property that allows you to move coefficients as exponents: \(a \log b = \log b^{a}\).
Apply this property to the term \(-3 \log x\), rewriting it as \(\log x^{-3}\).
Rewrite the expression using the property: \(\log 3 - \log x^{3}\).
Use the logarithmic subtraction property: \(\log a - \log b = \log \left( \frac{a}{b} \right)\) to combine into a single logarithm: \(\log \left( \frac{3}{x^{3}} \right)\).

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:
3m

Concetti chiave

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

Properties of Logarithms

Properties of logarithms include rules such as the product, quotient, and power rules. These allow us to combine or break down logarithmic expressions. For example, the power rule states that a coefficient in front of a log can be rewritten as an exponent inside the log.
Video consigliato:
5:36
Change of Base Property

Power Rule of Logarithms

The power rule states that a coefficient multiplied by a logarithm can be expressed as the logarithm of the argument raised to that coefficient. For instance, a·log_b(x) = log_b(x^a). This is essential for rewriting expressions to have a single logarithm.
Video consigliato:
5:50
Power Rules

Combining Logarithmic Expressions

To condense multiple logarithmic terms into one, use the product rule (log_b(M) + log_b(N) = log_b(M·N)) and quotient rule (log_b(M) - log_b(N) = log_b(M/N)). Applying these rules helps write the expression as a single logarithm with coefficient 1.
Video consigliato:
7:30
Logarithms Introduction
Pratica correlata
Domanda del libro di testo

Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of \$10,000 for 5 years at an interest rate of 1.32% if the money is b. compounded quarterly

1648
views
Domanda del libro di testo

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. log2(x+25)=4

790
views
Domanda del libro di testo

Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of \$10,000 for 5 years at an interest rate of 1.32% if the money is d. compounded continuously.

2908
views
Domanda del libro di testo

Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of \$10,000 for 5 years at an interest rate of 1.32% if the money is c. compounded monthly.

2602
views
Domanda del libro di testo

Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Suppose that you have \$12,000 to invest. Which investment yields the greater return over 3 years: 0.96% compounded monthly or 0.95% compounded continuously?

885
views
Domanda del libro di testo

Begin by graphing f(x) = log₂ x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range. h(x)=1+ log₂ x

732
views