Answer:
[tex]3\ln2 +6y=\ln(8e^{6y})[/tex]
Step-by-step explanation:
The given logarithmic expression is
[tex]3\ln2 +6y[/tex]
We can rewrite this as;
[tex]3\ln(2) +6y\ln(e)[/tex]
Recall and use the power rule of logarithms.
[tex]k\ln(a)=\ln(a^k)[/tex]
This gives us;
[tex]\ln(2^3) +\ln(e^{6y})[/tex]
[tex]\ln(8) +\ln(e^{6y})[/tex]
We now apply the product rule of logarithms;
[tex]\ln(a)+\ln(b)=\ln(ab)[/tex]
We apply this rule to get;
[tex]\ln(8e^{6y})[/tex]
