Show that i. logy √x . log z y^3 . log x 3√z^2 = 1

Question

Show that 

i. log_y\(\sqrt{x}\). log_z y³. log_x \(\sqrt[3]{z^2}=1\) 

ii. log_ba⁵ . log_cb³ . log_ac⁷ = 105 

iii. log_v\(\sqrt[4]{u^3}\) . log_wv⁵ . log_u\(\sqrt[5]{w^4}\) = 3.

Answer 1

i. L.H.S. = log_y\(\sqrt{x}\) . log_zy³ . log_x\(\sqrt[3]{z^2}\)

= 1 

= R.H.S.