Answer:
Explanation:
1. u^2 = x^(p+q)
v^2 = x^(p-q)
Show that logx u + logx v = p
From statement 1
p + q = logx u^2 = 2 logx u (by the laws of logs)
Similarly:
p - q = logx v^2 = 2 logx v
So 2 logx U + 2 logx v = p+q + (p - q)
2 (logx u + logx v) = 2p
logx u + logx v = p.
Also 2(logx u - logx v) = p+q - (p - q) = 2q
and logx u - logx v = q.
2. ∛(8a^3b^3) / √(1/25 * a^4b^7)* (16√(a^4b^6))^-1/2
= 2ab / 1/5a^2b^7/2 * (16a^2b^3)^-1/2
= 2ab / 1/5a^2b^7/2 * 1 / 4ab^3/2
= 2ab / 4/5 a^3 b^5
= 5ab / 2 a^3 b^5
= 5/(2a^2b^4).