Chapter 4.5, Problem 36E

Solution

To condense: The given logarithmic expression.

  $\ln x^6{y}^4$

Given:

An expression $6\ln x+4\ln y$.

Concept used:

If $m$ and $n$ are positive numbers then $\ln \left(mn\right)=\ln m+\ln n$ and $\ln m^n=n\ln m$ . These rules are known as product rule and power rule respectively.

Calculation:

  $6\ln x+4\ln y$

Apply the power rule.

  $\ln x^6+\ln y^4$

Apply the product rule.

  $\ln x^6{y}^4$

Conclusion:

The condensed logarithmic expression is $\ln x^6{y}^4$.