Ch. 4 - Exponential and Logarithmic Functions

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 4 - Exponential and Logarithmic Functions

Problema 89

Capitolo 5, Problema 89

Evaluate or simplify each expression without using a calculator. In e⁶

Guida verificata passo dopo passo

Step 1: Identify the expression to be simplified or evaluated. In this case, the expression is \( e^{6} \), which is the exponential function with base \( e \) raised to the power of 6.

Step 2: Recall the definition of the exponential function \( e^{x} \), where \( e \) is Euler's number (approximately 2.71828), and \( x \) is the exponent. The expression \( e^{6} \) means multiplying \( e \) by itself 6 times.

Step 3: Since the problem asks to simplify or evaluate without a calculator, recognize that \( e^{6} \) is already in its simplest exact form as an exponential expression.

Step 4: If the problem requires expressing \( e^{6} \) in terms of other expressions, consider using properties of exponents, such as \( e^{6} = (e^{3})^{2} \) or \( e^{6} = e^{2} \cdot e^{4} \), depending on the context.

Step 5: Conclude that \( e^{6} \) is best left as is unless further instructions are given, since it cannot be simplified into a simpler algebraic expression without approximating \( e \).

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:

Concetti chiave

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

Exponents and Powers

Exponents represent repeated multiplication of a base number. Understanding how to manipulate powers, such as multiplying, dividing, and raising powers to powers, is essential for simplifying expressions involving exponents without a calculator.

Video consigliato:

04:10

Powers of i

Properties of Exponents

The properties of exponents, including the product rule, quotient rule, and power rule, allow for the simplification of expressions by combining or breaking down powers. Mastery of these rules helps in rewriting expressions in simpler forms.

Video consigliato:

04:06

Rational Exponents

Simplification Techniques

Simplification involves reducing expressions to their simplest form by applying algebraic rules and properties. This includes factoring, canceling common terms, and rewriting expressions to avoid complex calculations, especially when calculators are not allowed.

Video consigliato:

04:15

Multiply Polynomials Using the Distributive Property

Pratica correlata

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. ln(x−4)+ln(x+1)=ln(x−8)

1194

views

Domanda del libro di testo

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log₄ (2x³) = 3 log₄ (2x)

787

views

Domanda del libro di testo

Evaluate or simplify each expression without using a calculator. In (1/e⁶)

803

views

Domanda del libro di testo

Evaluate or simplify each expression without using a calculator. In e

789

views

Domanda del libro di testo

Evaluate or simplify each expression without using a calculator. In 1