Convert each of the following to exponential form:

(i) log₃ 81 = 4

(ii) log₈ 4 = $\dfrac{2}{3}$

(iii) log₂ $\dfrac{1}{8}$ = -3

(iv) log₁₀ (0.01) = -2

(v) log₅ $\Big(\dfrac{1}{5}\Big)$ = -1

(vi) log_a 1 = 0

(i) Given,

⇒ log₃ 81 = 4

⇒ 3⁴ = 81.

Hence, exponential form is 3⁴ = 81.

(ii) Given,

⇒ log₈ 4 = $\dfrac{2}{3}$

⇒ $(8)^\dfrac{2}{3}$ = 4.

Hence, exponential form is $(8)^\dfrac{2}{3}$ = 4.

(iii) Given,

⇒ log₂ $\dfrac{1}{8}$ = -3

⇒ 2^-3 = $\dfrac{1}{8}$.

Hence, exponential form is 2^-3 = $\dfrac{1}{8}$.

(iv) Given,

⇒ log₁₀ (0.01) = -2

⇒ 10^-2 = 0.01.

Hence, exponential form is 10^-2 = 0.01.

(v) Given,

⇒ log₅ $\Big(\dfrac{1}{5}\Big)$ = -1

⇒ 5^-1 = $\Big(\dfrac{1}{5}\Big)$.

Hence, exponential form is 5^-1 = $\Big(\dfrac{1}{5}\Big)$.

(vi) Given,

⇒ log_a 1 = 0

⇒ a⁰ = 1.

Hence, exponential form is a⁰ = 1.