How to solve 3 variables problem with logarithm term

Question

Given three equation

$$\log{(2xy)} = (\log{(x)})(\log{(y)})$$ $$\log{(yz)} = (\log{(y)})(\log{(z)})$$ $$\log{(2zx)} = (\log{(z)})(\log{(x)})$$

Find the real solution of (x, y, z)

What should I do to get the answer? and I think it's not possible that x = y = z has a solution, I have no idea what method I can do. Show me a hint

Let $A=\log x, B=\log y, C=\log z$. Now use the properties of the log to rewrite your equations in terms of $A,B, C$. — lulu, Oct 26 '19 at 11:43
No, the equation is definetely written just like that in my book. And that's why I feel like there's a mistake in the question. — Anas Ghazi, Oct 26 '19 at 12:05

score 0 · Answer 1 · answered Oct 26 '19 at 11:46

0

Note that $\log abc = \log a + \log b + \log c$

If you then substitute $\log x = a$, $\log y = b$, $\log z = c$, you get an equation in $a, b, c$ which is easier to solve.

As suggested, I would check the second equation-is a 2 missing?

answered Oct 26 '19 at 11:46

John_dydx

score 0 · Answer 2 · answered Oct 26 '19 at 11:46

0

Set $a=\log x$, $b=\log y$, $c=\log z$ then solve

subtracting the first and the third

but $a=1$ is not acceptable then $b=c$.

answered Oct 26 '19 at 11:46

user

2 Answers2