How do you solve #3^(x+7)=4^x#?
When I see these types of problems, it's helpful for me to rewrite the equation such that the bases of the two exponentials are the same. What do I mean by this?
Well, the logarithm and the exponential are inverse functions, right? So, it's logical that 4 is actually the same thing as
Using this logic we can write the original equation as
And now, using some laws of exponentials, we can simplify the above equation as
Now, how does this help us? Well, we can now take the base-3 logarithm of both sides of the equation:
The logarithms will cancel with the exponentials, leaving us with
From here, we just need some simple algebra to solve for
And then divide:
And there is our answer.