Question

What is 3 log Subscript 2 Baseline x minus (log Subscript 2 Baseline 3 minus log Subscript 2 Baseline (x + 4)) written as a single logarithm?

Answer 1

Answer:

A.

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step explanation:

We have to write the following logarithmic expression as a single logarithm.

The given expression is

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

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

{Since, $\log A - \log B = \log \frac{A}{B}$, from the properties of logarithmic function }

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

{Since, $a\log b = \log b^{a}$, which also a logarithmic property}

= $\log_{2} [\frac{x^{3}}{\frac{3}{x + 4}}]$

= $\log_{2} [\frac{x^{3}(x + 4)}{3}]$ (Answer)