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: . This means the log of a quotient is the difference of the logs.
Substitute the given values: since and , replace these in the expression.
Write the expression as .
This expresses 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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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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.
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.