1 Answer

Oussama BEN MAHMOUD · Answer 1 · 2020-06-11T02:46:37+0000

Answer:

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

Explanation:

The given logarithmic expression;

$3\log_2x-(\log_23-\log_2(x+4))$

Expand the parenthesis:

$3\log_2x-\log_23+\log_2(x+4)$

Use the product rule on the last two terms;

$\log_aM+\log_aN=\log_aMN$

$3\log_2x-\log_23(x+4)$

Apply the power rule:

$\log_2x^3-\log_23(x+4))$

We now apply the quotient rule of logarithms:

$\log_aM+\log_aN=\log_a((M)/(N))$

$\log_2x^3-\log_23(x+4)=\log_2((x^3)/(3(x+4)))$

Or

$\log_2x^3-\log_23(x+4)=\log_2(((x^3)/(3))/(x+4))$

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