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Chapter 3: Problem 76

Condense the expression to the logarithm of a single quantity. $$2 \ln 8+5 \ln (z-4)$$

Short Answer

Expert verified
\(\ln (64 \cdot (z-4)^5)\)

Step by step solution

01

Applying the Power Rule

First, apply the power rule to both terms. According to this property, \(a \cdot \ln b = \ln (b^a)\). Using this rule, the expression becomes: \(\ln (8^2) + \ln ((z-4)^5) = \ln 64 + \ln (z-4)^5\)
02

Applying the Product Rule

Next, apply the product rule. This math property says that \(\ln a + \ln b = \ln (a \cdot b)\). Therefore, the expression becomes: \(\ln (64 \cdot (z-4)^5)\)

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Most popular questions from this chapter

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