Question

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

Answer 1

Answer:

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

Step-by-step 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

Answer:

$log_{2}(\frac{x^{3}(x+4)}{3})$.

Step-by-step explanation:

$3log_{2}x-(log_{2}3-log_{2}(x+4))$

$log_{2}x^{3}-log_{2}(\frac{3}{x+4})$

$log_{2}(\frac{x^{3}}{\frac{3}{x+4}})$

$log_{2}(\frac{x^{3}(x+4)}{3})$.