Question

\( \log _{y} \sqrt{x} \log _{z} y^{3} \log _{\sqrt{x^{3}}} \sqrt{z^{2}}= \)

Answer 1

log _y √ x  log _z y ³ log _{√ x ³} √ z ²    = ( log√ x)/(logy) (logy³)/(logz)  (log √ z ²)/(log√ x ³ )

=(1/2) { logx  (3) logy (2) logz }/{ logy  logz  (3) logx }

= { logx   logy  logz }/{ logy  logz   logx }  = 1