$Let$ $a,b,c>0$
$$\begin{cases}\log_a(b^x)=2\\\log_b(c^x)=2\\\log_c(a^x)=5\end{cases}$$
$$x=?$$
So my attempt is just to use the logarithmic definition:
$$\log_a(b^x)=2\iff b^x=a^2$$
By similar logic,
$$a^x=c^5$$ $$c^x=b^2$$
So, if add everything together, we should get:
$$a^x+b^x+c^x=a^2+b^2+c^5$$
Looks to me like x is equal 2 different numbers at the same time which is strange, what am I doing wrong here?
I'm going to be a maths student in the upcoming year, this is taken from the Tel-Aviv university preparation material - shouldn't be too complex.