Did I do this correctly?
Use log laws to write the following expression as a single logarithm.
3/2 ln25 + 3 ln2 = ln25 3/2 + ln2^3 = ln125 + ln2^3
=ln125 + ln8
=ln(125*8)
=ln1000
To determine if you simplified the expression correctly, let's go through the steps together.
Starting from the original expression: 3/2 ln25 + 3 ln2
1. Apply the power rule of logarithms to simplify ln2^3:
ln2^3 = ln(2*2*2) = ln8
2. Use the product rule of logarithms to combine ln125 and ln8:
ln125 + ln8 = ln(125*8)
3. Finally, apply the logarithmic rule to simplify ln(125*8):
ln(125*8) = ln(1000)
Therefore, your final answer should be ln1000. Based on the steps you provided, you have done it correctly. Well done!