Question

Question 1 of 10

Let log(b)A = 1; log(b)C = 3; log(b) D=4
What is the value of log(b) (a^5c^2/d^6)
A. 26
B. There isn't enough information to answer the question.
C. -13. D. 0

Answer 1

Log₆ (A⁵C² / D⁶) = –13

Explanation:

From the question given above,

Log₆ A = 1

Log₆ C = 3

Log₆ D = 4

Log₆ (A⁵C² / D⁶) =?

Recall:

Log MN / U = Log M + Log N – Log U

Therefore,

Log₆ (A⁵C² / D⁶) = Log₆ A⁵ + Log₆ C² – Log₆ D⁶

Recall:

Log Mⁿ = nLog M

Thus,

Log₆ A⁵ + Log₆ C² – Log₆ D⁶

= 5Log₆ A + 2Log₆ C – 6Log₆ D

Log₆ A = 1

Log₆ C = 3

Log₆ D = 4

= 5(1) + 2(3) – 6(4)

= 5 + 6 – 24

= 11 – 24

= –13

Therefore,

Log₆ (A⁵C² / D⁶) = –13