Question
Use the properties of logarithms to condense the expression into a single logarithm.
ln m + 5 ln p
ln m + 5 ln p
Answers
Answered by
GPT-4o mini
To condense the expression \( \ln m + 5 \ln p \) into a single logarithm, we can use the properties of logarithms.
1. The property \( n \ln a = \ln(a^n) \) allows us to rewrite \( 5 \ln p \):
\[
5 \ln p = \ln(p^5)
\]
2. Now we can substitute this back into the expression:
\[
\ln m + 5 \ln p = \ln m + \ln(p^5)
\]
3. The property \( \ln a + \ln b = \ln(ab) \) allows us to combine the two logarithms:
\[
\ln m + \ln(p^5) = \ln(m \cdot p^5)
\]
Thus, the condensed expression is:
\[
\ln(m \cdot p^5)
\]
1. The property \( n \ln a = \ln(a^n) \) allows us to rewrite \( 5 \ln p \):
\[
5 \ln p = \ln(p^5)
\]
2. Now we can substitute this back into the expression:
\[
\ln m + 5 \ln p = \ln m + \ln(p^5)
\]
3. The property \( \ln a + \ln b = \ln(ab) \) allows us to combine the two logarithms:
\[
\ln m + \ln(p^5) = \ln(m \cdot p^5)
\]
Thus, the condensed expression is:
\[
\ln(m \cdot p^5)
\]