How to solve this equation? $x$ can never be equal to $0$ nor its exponent. Am I right?
$\large x^{\log_x (x^2 + x - 2)}=0$
How to solve this equation? $x$ can never be equal to $0$ nor its exponent. Am I right?
$\large x^{\log_x (x^2 + x - 2)}=0$
HINT
Hint: $a^{log_a(b)}=b$ (to see why this is true look at mixdmath answer)
Since you are using $\log_x$, you must exclude $x = 0$ in the real or complex domain. Now let $w, z\in C$. Then we have $w^z = \exp(z L(w)), $ where $L$ is some branch of the logarithm. Note that $0$ is not in the range of the exponential function. Hence you are sunk here. There are no solutions, no matter what branch of the log you choose.
If you are in the real domain only, the logic is even simpler. You cannot raise a nonzero number to a power and get 0.