How do you solve 3^(x+1) + 3^x = 36?

1 Answer
Apr 21, 2016

x=2

Explanation:

First we to need to know a property of exponents with more than 1 term:
a^(b+c)=a^b*a^c
Applying this, you can see that:
3^(x+1)+3^x=36
3^x*3^1+3^x=36
3^x*3+3^x=36
As you can see, we can factor out 3^x:
(3^x)(3+1)=36
And now we rearrange so any term with x is on one side:
(3^x)(4)=36
(3^x)=9

It's should be easy to see what x should be now, but for the sake of knowledge (and the fact that there are much harder questions out there), I'll show you how to do it using log

In logarithms, there is a root which states: log(a^b)=blog(a), saying that you can move exponents out and down from the brackets. Applying this to where we left off:
log(3^x)=log(9)
xlog(3)=log(9)
x=log(9)/log(3)
And if you type it into your calculator you'll get x=2