If and , then is equal…

MATHEMATICS · Single correct · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

y=a^{\frac{1}{1-\log_a x}}

and

z=a^{\frac{1}{1-\log_a y}}

, then

x

is equal to: (1)

a^{\frac{1}{1+\log_a z}}

(2)

a^{\frac{1}{2+\log_a z}}

(3)

a^{\frac{1}{1-\log_a z}}

(4)

a^{\frac{1}{2-\log_a z}}