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

 

ln(125k)
 
 

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

 

ln(125k)=

To expand the logarithmic expression \( \ln(125k) \) as much as possible, we apply the properties of logarithms. Specifically, we use the product rule of logarithms, which states that:

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

Thus, for \( \ln(125k) \):

\[
\ln(125k) = \ln(125) + \ln(k)
\]

Now, since \( 125 = 5^3 \), we can further simplify \( \ln(125) \) using the power rule of logarithms, which states that:

\[
\ln(a^b) = b \cdot \ln(a)
\]

So,

\[
\ln(125) = \ln(5^3) = 3 \cdot \ln(5)
\]

Therefore, the fully expanded form is:

\[
\ln(125k) = 3 \cdot \ln(5) + \ln(k)
\]

This is the expanded logarithmic expression.

Would you like any more details or explanations?

Here are 5 related questions:
1. How do you apply the quotient rule of logarithms?
2. What is the logarithmic rule for division?
3. How would you expand \( \ln(100k^2) \)?
4. Can logarithms be applied to negative numbers?
5. What is the inverse operation of a logarithm?

**Tip:** When dealing with logarithms, always look for opportunities to apply the product, quotient, and power rules to simplify expressions.

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

ln(125k)

Learn how to expand the logarithmic expression ln(125k) using the product and power rules of logarithms. This step-by-step solution simplifies the expression as 3 * ln(5) + ln(k). Suitable for students in Grades 9-12.

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