Answer:
3. [tex]\log_6 4+5\log_6 a[/tex]
Step-by-step explanation:
Given:
The logarithm to expand is given as:
[tex]\log_6 4a^5[/tex]
We use the following property of logarithm to expand it into sum of 2 logarithms:
[tex]\log_b (xy)=\log_b x+\log_b y[/tex]
Therefore,
[tex]\log_6 4a^5[/tex] = [tex]\log_6 4+\log_6 a^5[/tex]
Now, we further simplify the second logarithm using the following property:
[tex]\log_b x^m=m\log_b x[/tex]
Therefore, [tex]\log_6 a^5=5\log_6 a[/tex]
This gives,
[tex]\log_6 4a^5[/tex] = [tex]\log_6 4+5\log_6 a[/tex]
Therefore, the correct choice is choice 3.