Convert each of the following to logarithmic form:

(i) 5² = 25

(ii) 3^-3 = $\dfrac{1}{27}$

(iii) $(64)^\dfrac{1}{3}$ = 4

(iv) 6⁰ = 1

(v) 10^-2 = 0.01

(vi) 4^-1 = $\dfrac{1}{4}$

(i) Given,

⇒ 5² = 25

⇒ log₅ (25) = 2.

Hence, logarithmic form is log₅ (25) = 2.

(ii) Given,

⇒ 3^-3 = $\dfrac{1}{27}$

⇒ log₃ $\Big(\dfrac{1}{27}\Big)$ = -3.

Hence, logarithmic form is log₃ $\Big(\dfrac{1}{27}\Big)$ = -3.

(iii) Given,

⇒ $(64)^\dfrac{1}{3}$ = 4

⇒ log₆₄ 4 = $\dfrac{1}{3}$.

Hence, logarithmic form is log₆₄ 4 = $\dfrac{1}{3}$.

(iv) Given,

⇒ 6⁰ = 1

⇒ log₆ 1 = 0.

Hence, logarithmic form is log₆ 1 = 0.

(v) Given,

⇒ 10^-2 = 0.01

⇒ log₁₀ (0.01) = -2.

Hence, logarithmic form is log₁₀ (0.01) = -2.

(vi) Given,

⇒ 4^-1 = $\dfrac{1}{4}$

⇒ log₄ $\dfrac{1}{4}$ = -1.

Hence, logarithmic form is log₄ $\dfrac{1}{4}$ = -1.