Expand using logarithmic properties

Question

Expand log₂(u²v³/w-6)

Answer 1

Expand: log₂(u²v³/w^-6).

Remember the division rule of logarithms: log_b(A/B) = log_b(A) - log_b(B).

So, log₂(u²v³/w^-6) = log₂(u²v³) - log₂(w^-6).

Now, remember the multiplication rule of logarithms for the first term: log_b(AB) = log_b(A) + log_b(B).

So, log₂(u²v³) - log₂(w^-6) = log₂(u²) + log₂(v³) - log₂(w^-6).

Now, remember the power rule of logarithms for all those terms: log_b(A)^r = r log_b(A).

And, you have your final answer: 2 log₂(u) +3 log₂(v) + 6 log₂(w).

Answer 2

log₂(u^2v^3/w^-6)

=log₂(u^2v^3w^6)

=log₂u^2 + log₂v^3 + log₂w^6

= 2log₂u + 3log₂v + 6log₂w

use rules of logs

logx^y = ylogx, power becomes a coefficient

logxy = logx +logy product becomes a sum

regardless of the base

Answer 3