Question

What is 3log2 x-(log2 3-log2 (x+4)) written as a single logarithm?

Answer 1

log_2((x^4+4x^3)/3)

Explanation:

First step would be distribute that - into the ( )

3log_2(x)-log_2(3)+log_2(x+4)

Now take care of coefficients of the logs... bring them up as powers of the inside

log_2(x^3)-log_2(3)+log_2(x+4)

or

+log_2(x^3)-log_2(3)+log_2(x+4)

Now for the product and quotient rule! If it has a + in front of it, it will go on top. If it has a - in front of it, it will go on bottom.

Like this:

log_2 (x^3(x+4)/3)

or

log_2((x^4+4x^3)/3)

So inside that log base 2 thing the top is x^4+4x^3

and that bottom is 3

Answer 2

`log_(2)((x^(3)(x+4))/(3))`.

Explanation:

`3log_(2)x-(log_(2)3-log_(2)(x+4))`

`log_(2)x^(3)-log_(2)((3)/(x+4))`

`log_(2)((x^(3))/((3)/(x+4)))`

`log_(2)((x^(3)(x+4))/(3))`.