annistont
annistont annistont
  • 12-06-2019
  • Mathematics
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what is 3log(2)3-log(2)(x+4) written as a single logarithm

what is 3log23log2x4 written as a single logarithm class=

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gmany
gmany gmany
  • 20-06-2019

Answer:

[tex]\large\boxed{\log_2\dfrac{x^3}{\left(\dfrac{3}{x+4}\right)}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\\log_ab^n=n\log_ab\\\\\log_a\left(\dfrac{c}{d}\right)=\log_ac-\log_ad\\\\==============================[/tex]

[tex]\text{We have:}\\\\3\log_2x-(\log_23-\log_2(x+4))\\\\=\log_2x^3-\log_2\dfrac{3}{x+4}\\\\=\log_2\dfrac{x^3}{\frac{3}{x+4}}[/tex]

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