If x= log 2 3-4 log ( ln (5/4))2 3, y= log √3( ln (5/4)) and z= log 2( log (5 / 4) e) then find the absolute value of (x y+2 z)

Question

If x= log 2 3-4 log ( ln (5/4))2 3, y= log √3( ln (5/4)) and z= log 2( log (5 / 4) e) then find the absolute value of (x y+2 z) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

xy +2 z =( log 2 3-4 log ( ln (5/4))3 3) 2 log 3( ln (5/4))+2 log 2( log (5/4) e ) =2 log 2( ln (5/4))-8-2 log 2( ln (5/4))=-8 ∴ |x y+2 z|=8

Q. If $x = lo g_{2} 3 - 4 lo g_{(l n \frac{5}{4})^{2}} 3, y = lo g_{3} (ln \frac{5}{4})$ and $z = lo g_{2} (lo g_{(5/4)} e)$ then find the absolute value of $(x y + 2 z)$