Write each expression as a single logarithm with coefficient I. Assume all variables represent p

step 1 Okay, so we're just going to be rewriting this sum of logarithms into one logarithm. And so here

Write each expression as a single logarithm with coefficient...

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Key Concepts

Logarithmic Quotient Rule

The logarithmic quotient rule states that the difference between two logarithms with the same base can be written as the logarithm of the quotient of their arguments. That is, log_b(M) - log_b(N) = log_b(M / N). This rule is used to combine terms that are subtracted in logarithmic expressions, simplifying them into a single logarithmic form.

Logarithmic Product Rule

The logarithmic product rule states that the sum of two logarithms with the same base can be written as the logarithm of the product of their arguments. Mathematically, log_b(M) + log_b(N) = log_b(M * N). This property is vital when combining terms that are added together in logarithmic expressions.

Properties of Logarithms

Logarithms have several key properties that allow us to combine multiple logarithmic expressions into a single one. Two important properties are the product rule and the quotient rule, which are essential when rewriting sums and differences of logarithms as a single logarithm.

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