Answer:
[tex]\log_{2} [\frac{x^{3}(x + 4)}{3}][/tex]
Step-by-step explanation:
We have to write the following logarithmic expression as a single logarithm.
The given expression is
[tex]3\log_{2} x - [\log_{2} 3 - \log_{2}(x + 4)][/tex]
= [tex]3\log_{2} x - \log_{2} (\frac{3}{x + 4})[/tex]
{Since, [tex]\log A - \log B = \log \frac{A}{B}[/tex], from the properties of logarithmic function }
= [tex]\log_{2} x^{3} - \log_{2} (\frac{3}{x + 4})[/tex]
{Since, [tex]a\log b = \log b^{a}[/tex], which also a logarithmic property}
= [tex]\log_{2} [\frac{x^{3}}{\frac{3}{x + 4}}][/tex]
= [tex]\log_{2} [\frac{x^{3}(x + 4)}{3}][/tex] (Answer)
