Question

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)))

Answer 1

-11

Explanation:

Given

`\log_bA=3\\ \\\log_bC=2\\ \\\log_bD=5`

Use properties:

`\log_b(A\cdot C)=\log_bA+\log_bC\\ \\\log_b(A)/(C)=\log_bA-\log_bC\\ \\\log_bA^k=k\log_bA`

Thus,

`\log_b(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`