Let log (A) = − 8 , log (B) = 1 , and log (C) = 9 . Evaluate the following logarithms using logarithmic properties.

Question

Let log (A) = − 8 , log (B) = 1 , and log (C) = 9 . Evaluate the following logarithms using logarithmic properties.

log(a^5/√b) =

log (b/c^3) =

log (a/b^4c) =

please give answer and explain i'm havin trouble with this topic

Answer 1

(1)     5 log a – ½ log b = 5(-8) – ½ (1) = -40 – ½ = -40 ½

(2)   Log b – 3 log c = 1 – 3(9) = 1 – 27 = -26

(3)   Log a – 4 log b – log c = -8 – 4(1) – 9 = -8-4-9 = -21

There are 3 properties of logarithms involved here, that are being used in combination:

property #1: Log(MN) = log M + log N

property #2: Log(M/N) = log M - log N

property #3: Log(M^k) = k * Log M

Note that property 1 can be applied repeatedly to any number of terms in the product of the argument in the log. That is log (ABCD...XYZ) = log A + log B + log C ... + log X + logY + log Z