Question
Suppose that \( \ln 2=s \) and \( \ln 3=t \). Use properties of logarithms to write the logarithm in terms of 5 and \( t \). \( \ln 6 \)
Ask by Carlson Fernandez. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \ln 6 = s + t \)
Solution
Given that \( \ln 2 = s \) and \( \ln 3 = t \), we want to express \( \ln 6 \) in terms of \( s \) and \( t \).
First, observe that \( 6 \) can be factored into \( 2 \times 3 \). Using the property of logarithms that states \( \ln(ab) = \ln a + \ln b \), we have:
\[
\ln 6 = \ln(2 \times 3) = \ln 2 + \ln 3
\]
Substituting the given values:
\[
\ln 6 = s + t
\]
**Answer:** \( \ln 6 = s + t \)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Extra Insights
To express \( \ln 6 \) using the given variables, we can use the property \( \ln(ab) = \ln a + \ln b \). Since \( 6 = 2 \times 3 \), we have: \[ \ln 6 = \ln(2 \times 3) = \ln 2 + \ln 3 = s + t. \] Now, substituting \( \ln 2 = s \) and \( \ln 3 = t \), we can write: \[ \ln 6 = s + t. \] This means that \( \ln 6 \) can be expressed as the sum of \( s \) and \( t \).
