jackiekresek jackiekresek
  • 03-01-2020
  • Mathematics
contestada

Let log_(b)A=3; log_(b)C=2; log_(b)D=5 what is the value of log_(b)((A^(5)C^(2))/(D^(6)))

Respuesta :

frika
frika frika
  • 10-01-2020

Answer:

-11

Step-by-step explanation:

Given

[tex]\log_bA=3\\ \\\log_bC=2\\ \\\log_bD=5[/tex]

Use properties:

[tex]\log_b(A\cdot C)=\log_bA+\log_bC\\ \\\log_b\dfrac{A}{C}=\log_bA-\log_bC\\ \\\log_bA^k=k\log_bA[/tex]

Thus,

[tex]\log_b\dfrac{A^5\cdot C^2}{D^6}\\ \\=\log_b(A^5\cdot C^2)-\log_bD^6\\ \\=\log_bA^5+\log_bC^2-\log_bD^6\\ \\=5\log_bA+2\log_bC-6\log_bD\\ \\=5\cdot 3+2\cdot 2-6\cdot 5\\ \\=15+4-30\\ \\=-11[/tex]

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