Equation from Question:
$$x^{(\log_3(x))^2 + \log_3(x^4)-3}=3^{2\log_3(x)}$$
The question states to find the number of solutions and the sum of integral solutions. The correct answer is 3 solutions of integral sum 4
Solution attempt
According to my solution, I only get two solutions out of which only one is integral (3). Please help me in finding the mistake.
PS: Sorry for not typing the equation but I don't know how to do so on phone! Also, Stack wouldn't let me post images because of repo.
Let $t=\log_3 x$. Then,on taking $\log_3$ on both sides, we get - $$(t^2+4t-3)t=2t$$ Simplifying, we get $t=0,1,-5$, or $x=1,3,3^{\frac{1}{5}}$. Hence, sum of integral solutions $=4$