Question

For any positive numbers a, b, and d, with b≠1, logb(a·d) = _____.

Answer 1

logb a* logb d

or

logb a - logb d

or

logb(a*d)

Answer 2

The value of
`log_b(a\cdot d)` is
`log_b(a)+log_b(d)`.

Explanation:

Let a, b, and d are positive numbers.

Then we need to find the value of
`log_b(a\cdot d)`.

According to the multiplication property of logarithm.
`log_m(xy)=log_mx+log_my`

The given expression is

`log_b(a\cdot d)`

Using the multiplication property of logarithm, we get

`log_b(a\cdot d)=log_b(a)+log_b(d)`

Therefore the value of
`log_b(a\cdot d)` is
`log_b(a)+log_b(d)`.