What is the value of log(ab^2) - log(ac) + log(abc^4) - 3log(bc)?Question 6Answera.1b.0c.3d.2

To solve this problem, we need to use the properties of logarithms.

The properties are as follows:

1. log(a * b) = log(a) + log(b)
2. log(a / b) = log(a) - log(b)
3. log(a^n) = n * log(a)

Let's apply these properties to the given expression:

log(ab^2) - log(ac) + log(abc^4) - 3log(bc)

First, we can combine the logs using the properties:

= log(ab^2 / ac) + log(abc^4 / (bc)^3)

Simplify the expressions inside the logs:

= log(b) + log(a^2c)

Now, we can combine these two logs:

= log(b * a^2c)

Simplify the expression inside the log:

= log(a^2b^2c^2)

Now, we can use the third property of logarithms to bring down the exponents:

= 2log(a) + 2log(b) + 2log(c)

= 2(log(a) + log(b) + log(c))

= 2log(abc)

So, the value of the given expression is 2log(abc). Therefore, the answer is (d) 2.