turkey-yks 2016 Q30

turkey-yks · Other · lys1-math Laws of Logarithms Prove a Logarithmic Identity
Let t be a real number. The equalities
$$\begin{aligned} & x = e ^ { 2 \cos t } \\ & y = e ^ { 3 \sin t } \end{aligned}$$
are given.
Accordingly, which of the following gives the relationship between $x$ and y that is satisfied for every real number t?
A) $\ln ^ { 2 } x + \ln ^ { 2 } y = 4$
B) $\ln ^ { 2 } x + \ln ^ { 2 } y = 9$
C) $9 \ln ^ { 2 } x + 2 \ln ^ { 2 } y = 27$
D) $\ln ^ { 2 } x + 4 \ln ^ { 2 } y = 28$
E) $9 \ln ^ { 2 } x + 4 \ln ^ { 2 } y = 36$
Let t be a real number. The equalities

$$\begin{aligned}
& x = e ^ { 2 \cos t } \\
& y = e ^ { 3 \sin t }
\end{aligned}$$

are given.

Accordingly, which of the following gives the relationship between $x$ and y that is satisfied for every real number t?\\
A) $\ln ^ { 2 } x + \ln ^ { 2 } y = 4$\\
B) $\ln ^ { 2 } x + \ln ^ { 2 } y = 9$\\
C) $9 \ln ^ { 2 } x + 2 \ln ^ { 2 } y = 27$\\
D) $\ln ^ { 2 } x + 4 \ln ^ { 2 } y = 28$\\
E) $9 \ln ^ { 2 } x + 4 \ln ^ { 2 } y = 36$