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Write each equation in its equivalent logarithmic form. 132 = x
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Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 5, Problema 15
Write each equation in its equivalent exponential form. log3 81 = y
Guida verificata passo dopo passo1
Recall the definition of logarithm: \( \log_b a = c \) means \( b^c = a \).
Identify the base \( b \), the result \( a \), and the logarithm value \( c \) from the equation \( \log_3 81 = y \). Here, \( b = 3 \), \( a = 81 \), and \( c = y \).
Rewrite the logarithmic equation \( \log_3 81 = y \) in its equivalent exponential form using the definition: \( 3^y = 81 \).
This expresses the original logarithmic equation as an exponential equation, which is the required equivalent form.
You can verify this by recognizing that \( 81 \) is a power of \( 3 \), but the problem only asks for the equivalent exponential form, so no further calculation is needed.
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Definition of Logarithms
A logarithm answers the question: to what exponent must the base be raised to produce a given number? For example, log3 81 = y means 3 raised to the power y equals 81. Understanding this definition is essential to convert between logarithmic and exponential forms.
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Logarithms Introduction
Exponential Form of a Logarithmic Equation
The exponential form of a logarithmic equation log_b a = c is b^c = a. This conversion is fundamental because it allows solving logarithmic equations by rewriting them as exponential equations, making it easier to find unknown exponents or values.
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5:02Solving Logarithmic Equations
Properties of Exponents and Powers
Recognizing powers of numbers helps simplify and solve equations. For instance, knowing that 81 = 3^4 allows you to rewrite log3 81 = y as 3^y = 3^4, leading to y = 4. Familiarity with exponent rules aids in identifying equivalent expressions.
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04:10Powers of i
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