2 Answers

Bradley Slavik · Answer 1 · 2021-07-04T16:48:47+0000

Answer:

$\log_(2) [(x^(3)(x + 4))/(3)]$

Explanation:

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

The given expression is

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

=
$3\log_(2) x - \log_(2) ((3)/(x + 4))$

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

=
$\log_(2) x^(3)  - \log_(2) ((3)/(x + 4))$

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

=
$\log_(2) [(x^(3))/((3)/(x + 4))]$

=
$\log_(2) [(x^(3)(x + 4))/(3)]$ (Answer)

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