Power functions question and solving the equation. I'm translating this from my mother tongue so bear with me -
I have a question in relation to power functions but I think the problem I am dealing with is my seemingly lack of other mathematical rules that I need!
The equation I want to solve is:
$$7\cdot 5^x = 9-6\cdot 5^x$$
Now I know I can't just simplify it by subtracting $6$ from $9$, because of the product rule $-6\cdot 5^x$. Then, I tried to put $-6\cdot 5^x$ to the left side:
$$\frac{7\cdot 5^x}{-6\cdot 5^x} = 9$$
I think that's right, since the opposite of a product is division so I don't need to switch up the minus sign. But then I don't know what follows.. could someone please break it down for me

Let $5^x$ be $y$.
Now the question becomes $$7y = 9-6y$$
This is a linear equation, we would collect all the terms containing $y$ at one side.
$$7y+6y=9$$
You should be able to obtain
$$y=\frac{9}{13}.$$
Hence $$5^x=\frac9{13}$$
Now use logarithm to solve your question.
