Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.

 

ln(19k)
 
 

Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example,  c*ln(h)
 .

 

ln(19k)=
   

To expand the logarithmic expression \( \ln(19k) \), you can apply the logarithm product rule, which states:

\[
\ln(ab) = \ln(a) + \ln(b)
\]

For \( \ln(19k) \), treat \( 19k \) as the product of 19 and \( k \). Applying the product rule:

\[
\ln(19k) = \ln(19) + \ln(k)
\]

Thus, the expanded form is:

\[
\ln(19k) = \ln(19) + \ln(k)
\]

Would you like any further clarification on this?

Here are 5 related questions to explore:
1. How would you expand \( \ln(7x^2) \)?
2. Can you apply the same rule to \( \ln(a^2b^3) \)?
3. How does the logarithm of a quotient expand?
4. What is the expansion of \( \ln(10p^3q) \)?
5. How can you simplify \( \ln(1) \)?

**Tip:** Always remember the logarithm properties when simplifying expressions, especially the product, quotient, and power rules.

Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.

ln(19k)

Enclose arguments of functions in parentheses and include a multiplication sign between terms.

Learn how to expand the logarithmic expression ln(19k) by applying the product rule for logarithms. This problem demonstrates the use of fundamental algebraic properties of logarithms and is suitable for students in Grades 9-12.

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