Expand the following.

(i) log1000

(ii)

(iii) logx²y³z⁴

(iv)

(v)

Write the following expressions as log N and find their values.

(i) log2 + log5

(ii) log₂16 – log₂2

(iii) 3 log₆₄ 4

(iv) 2 log3 – 3 log 2

(v) log 10 + 2 log 3 – log 2

Evaluate each of the following in terms of x and y, if it is given x = log₂3 and y = log₂5

(i) log₂ 15 (ii) log₂7.5

(iii) log₂60 (iv) log₂6750

If x² + y² = 25xy, then prove that 2 log(x + y) = 3log3 + logx + logy.

If then find the value of