Sorry for not being clear with the form in the question.
I am struggling with this question, and I'm not sure where to start. Do you change the $3^{2x}/3^x$ in log form? My teacher didn't explain this lesson quite well so I don't understand how to do these type of questions.
The task you were given is to solve the following equation by using logarithms:
$$3^{2x} + 5*3^x - 14 = 0$$
The first step is to recognize that by changing variables, from $x$ to $y = 3^x$, one can obtain a quadratic equation:
$$y^2 + 5y - 14 = 0$$
We can solve this in the usual way, and obtain two solutions: $y = 2$ and $y= -7$. To rewrite this in terms of our original variable, $x$, we use the logarithm. But we can only apply it to the case $y = 2$, since a power of $3$ can not be a negative number. We get: $x = \log_3(2)$.
