How do you solve #2^ { - 2x + 3} = 8^ { - x }#?
1 Answer
Explanation:
By using logarithms. Logarithms have many properties that are interesting in solving problems like this. We will focus on three particular ones here:
1)
2)
3)
So, in context:
- property 1 tells us that a log of base
- property 2 tells us that a log of base
- property 3 tells us that a log of base
First we "log" both sides, using base 2:
Using property 3 lets us throw both exponents to the front:
Now we can rewrite 8 as 2 to the power of 3 and use the first rule on the left side's log and the second rule on the right side's log, leaving us with:
Now we just solve for x: