Answer:
The value of [tex]log_b(a\cdot d)[/tex] is [tex]log_b(a)+log_b(d)[/tex].
Step-by-step explanation:
Let a, b, and d are positive numbers.
Then we need to find the value of [tex]log_b(a\cdot d)[/tex].
According to the multiplication property of logarithm.[tex]log_m(xy)=log_mx+log_my[/tex]
The given expression is
[tex]log_b(a\cdot d)[/tex]
Using the multiplication property of logarithm, we get
[tex]log_b(a\cdot d)=log_b(a)+log_b(d)[/tex]
Therefore the value of [tex]log_b(a\cdot d)[/tex] is [tex]log_b(a)+log_b(d)[/tex].
