- #1

- 14

- 3

- Homework Statement
- Write this in a form not involving logarithm.

- Relevant Equations
- $$\log_x(y)=1/\log_y(x)$$

log

Solution

$$\begin{align*}\log_{ y }{ x } + \log_{ x }{ y } &= \frac{ 3 }{ 2 } \\

\log_{ x }{ y } &= \frac{ \log_{ y }{ y } }{ \log_{ y }{ x } } \\

\log_{ y }{ x } + \frac{ 1 }{ \log_{ y }{ x } } &= \frac{ 3 }{ 2 } \\

\left(\log_{ y }{ x } \right)^ { 2 } + 1 &= \frac{ 3 }{ 2 } \left(\log_{ y }{ x } \right) \\

\left(\log_{ y }{ x } \right) ^ { 2 } &= \frac{ 3 }{ 2 } \left(\log_{ y }{ x }\right) - 1

\end{align*}$$

What do I do next?

_{y}x + log_{x}y = 3/2Solution

$$\begin{align*}\log_{ y }{ x } + \log_{ x }{ y } &= \frac{ 3 }{ 2 } \\

\log_{ x }{ y } &= \frac{ \log_{ y }{ y } }{ \log_{ y }{ x } } \\

\log_{ y }{ x } + \frac{ 1 }{ \log_{ y }{ x } } &= \frac{ 3 }{ 2 } \\

\left(\log_{ y }{ x } \right)^ { 2 } + 1 &= \frac{ 3 }{ 2 } \left(\log_{ y }{ x } \right) \\

\left(\log_{ y }{ x } \right) ^ { 2 } &= \frac{ 3 }{ 2 } \left(\log_{ y }{ x }\right) - 1

\end{align*}$$

What do I do next?

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