Solving $9^{1+\log x} - 3^{1+\log x} - 210 = 0$ where base of log is $3$ for $x$

Question

Question is to solve the equation for value of $x$.

$$9^{1+\log x} - 3^{1+\log x} - 210 = 0; \quad \text{where base of log is }3$$

The answer given is $x=5$

I've tried to solve it. And got two values of $x= -14/3$ and $x=5$. What I've done wrong?

Answer 1

You have solved correctly just made one error towards the end. Note that the domain of $\log(x)$ is $x > 0$ so $x=-14/3$ is rejected as it is not in the domain of the function.