Answer:
[tex]\log_2(\frac{\frac{x^3}{3}}{x+4})[/tex]
Step-by-step explanation:
The given logarithmic expression;
[tex]3\log_2x-(\log_23-\log_2(x+4))[/tex]
Expand the parenthesis:
[tex]3\log_2x-\log_23+\log_2(x+4)[/tex]
Use the product rule on the last two terms;
[tex]\log_aM+\log_aN=\log_aMN[/tex]
[tex]3\log_2x-\log_23(x+4)[/tex]
[tex]3\log_2x-\log_23(x+4)[/tex]
Apply the power rule:
[tex]\log_2x^3-\log_23(x+4))[/tex]
We now apply the quotient rule of logarithms:
[tex]\log_aM+\log_aN=\log_a(\frac{M}{N})[/tex]
[tex]\log_2x^3-\log_23(x+4)=\log_2(\frac{x^3}{3(x+4)})[/tex]
Or
[tex]\log_2x^3-\log_23(x+4)=\log_2(\frac{\frac{x^3}{3}}{x+4})[/tex]
