By converting to exponential form, find the value of each of the following:

(i) log₂ 64

(ii) log₈ 32

(iii) log₃ $\dfrac{1}{9}$

(iv) log_0.5 (16)

(v) log₂ (0.125)

(vi) log₇ 7

Find the value of x, when:

(i) log₂ x = -2

(ii) log_x 9 = 1

(iii) log₉ 243 = x

(iv) log₃ x = 0

(v) $\log _{\sqrt{3}}$ (x − 1) = 2

(vi) log₅ (x² − 19) = 3

(vii) log_x 64 = $\dfrac{3}{2}$

(viii) log₂ (x² − 9) = 4

(ix) log_x (0.008) = −3

Given log₁₀ x = a, log₁₀ y = b,

(i) Write down 10^{a + 1} in terms of x.

(ii) Write down 10^2b in terms of y.

(iii) If log₁₀ P = 2a − b, express P in terms of x and y.

Evaluate the following without using log tables :

2 log 5 + log 8 − $\dfrac{1}{2}$ log 4