# How do you solve #3^(x+7)=4^x#?

##### 1 Answer

or, alternatively,

#### Explanation:

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

Factor

And then divide:

And there is our answer.