If log 3 5=x and log 25 11=y then the value of log 3((11/3)) in terms of x and y is

Question

If log 3 5=x and log 25 11=y then the value of log 3((11/3)) in terms of x and y is (A) x2 y-1 (B) 2 x y-1 (C) 2 x y+1 (D) (2 y-x/x)

Tardigrade Admin · Accepted Answer

log 3 5= x ⇒ 3 x =5 ⇒ 51 / x =3 ....(1) text and log 25 11=( log 5 11/2)= y ∴ log 5 11=2 y ⇒ 52 y =11 ....(2) (2 ÷ 1) ⇒ (11/3)=52 y-(1/x)=5(2 x y-1/x) log 3((11/3))=(2 x y-1/x) log 3 5=(2 x y-1/x) ⋅ x=2 x y-1 .

Q. If $lo g_{3} 5 = x$ and $lo g_{25} 11 = y$ then the value of $lo g_{3} (\frac{11}{3})$ in terms of $x$ and $y$ is

$x^{2} y - 1$

$2 x y - 1$

$2 x y + 1$

$\frac{2 y - x}{x}$

Q. If log3​5=x and log25​11=y then the value of log3​(311​) in terms of x and y is

x2y−1

2xy−1

2xy+1

x2y−x​

log3​5=x⇒3x=5⇒51/x=3 ....(1) and log25​11=2log5​11​=y ∴log5​11=2y⇒52y=11....(2) (2÷1)⇒311​=52y−x1​=5x2xy−1​ log3​(311​)=x2xy−1​log3​5=x2xy−1​⋅x=2xy−1.

Q. If $lo g_{3} 5 = x$ and $lo g_{25} 11 = y$ then the value of $lo g_{3} (\frac{11}{3})$ in terms of $x$ and $y$ is

$x^{2} y - 1$

$2 x y - 1$

$2 x y + 1$

$\frac{2 y - x}{x}$