what is $3\\log_2x-(\\log_23 - \\log_2(x + 4))$ written as a single logarithm?\n$\\log_2\\left\\frac{x^3(x +…

what is $3\\log_2x-(\\log_23 - \\log_2(x + 4))$ written as a single logarithm?\n$\\log_2\\left\\frac{x^3(x + 4)}{3}\\right$\n$\\log_2\\left(\\frac{3x^3}{x + 4}\\right)$\n$\\log_2\\left\\frac{x^3}{3(x + 4)}\\right$\n$\\log_2\\left(\\frac{x^3}{3+(x + 4)}\\right)$

what is $3\\log_2x-(\\log_23 - \\log_2(x + 4))$ written as a single logarithm?\n$\\log_2\\left\\frac{x^3(x + 4)}{3}\\right$\n$\\log_2\\left(\\frac{3x^3}{x + 4}\\right)$\n$\\log_2\\left\\frac{x^3}{3(x + 4)}\\right$\n$\\log_2\\left(\\frac{x^3}{3+(x + 4)}\\right)$

Answer

Explanation:

Step1: Apply power - rule of logarithms

$3\log_2x=\log_2x^3$

Step2: Apply quotient - rule of logarithms

$\log_23-\log_2(x + 4)=\log_2\frac{3}{x + 4}$

Step3: Rewrite the original expression

$3\log_2x-(\log_23-\log_2(x + 4))=\log_2x^3-\log_2\frac{3}{x + 4}$

Step4: Apply quotient - rule again

$\log_2x^3-\log_2\frac{3}{x + 4}=\log_2\frac{x^3}{\frac{3}{x + 4}}=\log_2\frac{x^3(x + 4)}{3}$

Answer:

$\log_2\left[\frac{x^3(x + 4)}{3}\right]$