Answer :
The correct answer is b) Log₅ uv⁶/u⁹).
Apply the power rule of logarithms: n log_b(x) = log_b([tex]x^n[/tex]).
This gives us: log₅((uv²/u³a)³).
Simplify the expression inside the logarithm: (uv²/u³a)³ = (u/u³ * v²/a)³ = ([tex]u^1/u^3 * v^2[/tex]/a)³ = [tex]u^{-2}[/tex]v²[tex]a^{-1}^3[/tex] = [tex]u^(-6)v^6a^{-3).[/tex]
Now, we have: log₅[tex](u^{-6}v^6a^{-3}).[/tex]
Thus, the expression simplified to a single logarithm is: log₅ u⁻⁶v⁶a⁻³, which can be further simplified to log₅ (v⁶/u⁶a³). So, the correct choice is (b) Log₅ uv⁶/u⁹).