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Chapter 12: Problem 121

Write as a single term that does not contain a logarithm: $$e^{\ln 8 x^{5}-\ln 2 x^{2}}$$

Short Answer

Expert verified
The simplified form of the expression \(e^{\ln 8 x^{5}-\ln 2 x^{2}}\) is \(4x^{3}\).

Step by step solution

01

Application of Difference of Logarithms Rule

Use the rule for difference of logarithms to combine \(\ln 8 x^{5} - \ln 2 x^{2}\) into \(\ln ((8 x^{5})/(2 x^{2}))\). This simplifies to \(\ln (4x^{3})\). So the expression becomes \(e^{\ln 4x^{3}}\).
02

Application of Exponential Law

Then, apply the exponential law to the expression \(e^{\ln 4x^{3}}\). Per the law \(e^{\ln a} = a\), the expression simplifies to \(4x^{3}\).

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