tmua 2022 Q15

tmua · Uk · paper2 1 marks Laws of Logarithms Express One Logarithm in Terms of Another
The real numbers $x , y$ and $z$ are all greater than 1 , and satisfy the equations
$$\log _ { x } y = z \quad \text { and } \quad \log _ { y } z = x$$
Which one of the following equations for $\log _ { z } x$ must be true?
A $\quad \log _ { z } x = y$
B $\quad \log _ { z } x = \frac { 1 } { y }$
C $\log _ { z } x = x y$
D $\log _ { z } x = \frac { 1 } { x y }$
E $\quad \log _ { z } x = x z$ F $\log _ { z } x = \frac { 1 } { x z }$ G $\log _ { z } x = y z$ H $\log _ { z } x = \frac { 1 } { y z }$
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The real numbers $x , y$ and $z$ are all greater than 1 , and satisfy the equations

$$\log _ { x } y = z \quad \text { and } \quad \log _ { y } z = x$$

Which one of the following equations for $\log _ { z } x$ must be true?\\
A $\quad \log _ { z } x = y$\\
B $\quad \log _ { z } x = \frac { 1 } { y }$\\
C $\log _ { z } x = x y$\\
D $\log _ { z } x = \frac { 1 } { x y }$\\
E $\quad \log _ { z } x = x z$\\
F $\log _ { z } x = \frac { 1 } { x z }$\\
G $\log _ { z } x = y z$\\
H $\log _ { z } x = \frac { 1 } { y z }$