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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 83
Capitolo 5, Problema 83

In Exercises 83–88, let logb 2 = A and logb 3 = C and Write each expression in terms of A and C.
logb (3/2)

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Recall the logarithm property for division: logb(32) = logb3 - logb2. This means the log of a quotient is the difference of the logs.
Substitute the given values: since logb2 = A and logb3 = C, replace these in the expression.
Write the expression as logb(32) = C - A.
This expresses logb(32) entirely in terms of the variables A and C as requested.
No further simplification is needed since the problem asks only to write the expression in terms of A and C.

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Properties of Logarithms

Logarithms have specific properties that simplify expressions, such as the quotient rule: log_b(x/y) = log_b(x) - log_b(y). This allows us to rewrite complex logarithmic expressions as differences or sums of simpler logs.
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Change of Base Property

Change of Base and Logarithm Notation

Understanding the notation log_b(x) means the logarithm of x with base b is crucial. Given log_b(2) = A and log_b(3) = C, we can express other logarithms with base b in terms of A and C by applying logarithmic properties.
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Change of Base Property

Expressing Logarithmic Expressions in Terms of Variables

When given variables representing logarithms, such as A and C, the goal is to rewrite expressions like log_b(3/2) using these variables. This involves substituting and simplifying using known values and logarithmic rules.
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Radical Expressions with Variables
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