SOLUTION: What is the solution for 8w/exponent or power of 2x+1=4w/exponent or power of 1-x? I've tried dividing the whole numbers by 4 first and I get -1/3, multiplying both sides of the e

Algebra ->  Exponents -> SOLUTION: What is the solution for 8w/exponent or power of 2x+1=4w/exponent or power of 1-x? I've tried dividing the whole numbers by 4 first and I get -1/3, multiplying both sides of the e      Log On


   

Question 248660: What is the solution for 8w/exponent or power of 2x+1=4w/exponent or power of 1-x? I've tried dividing the whole numbers by 4 first and I get -1/3, multiplying both sides of the exponents out first and then solving it and I get -3/5, and subtracting the exponents first which gave me 1/6, none of which get me the correct answer of -1/8. Yesterday I somehow got -1/4 for the answer but I forget how. I'm studying for the ACT.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
8%5E%282x%2B1%29+=+4%5E%281-x%29
The key to a relatively simple solution is to realize that both 8 and 4 are powers of two. This helps because is we can express everything as powers of the same base, the solution is easier. So we'll start by replacing 2%5E3 for 8 and 2%5E2 for 4:
%282%5E3%29%5E%282x%2B1%29+=+%282%5E2%29%5E%281-x%29
Now we can use the rule for exponents, %28a%5Ep%29%5Eq+=+a%5E%28p%2Aq%29, to simplify the exponents:
2%5E%283%2A%282x%2B1%29%29+=+2%5E%282%2A%281-x%29%29
2%5E%286x%2B3%29+=+2%5E%282-2x%29
Now the equation is in one of the forms we use to solve equations where the variable is in the exponent: some base to one power equal the same base to another power. (If we cannot get this type of equation into this form, then we generally use logarithms to solve it.) If 2 to the (6x+3) power equals 2 to the (2-2x) power, then
6x+3 = 2 - 2x
Now the variable is out of the exponents and we have a fairly simple equations to solve. Add 2x to each side:
8x + 3 = 2
Subtract 3 from each side:
8x = -1
Divide both sides by 8:
x+=+%28-1%29%2F8