SOLUTION: Without using a calculator, solve for x: a) 8^x = 1/ sqrt( 2 ) b) 4^2x+1 = (1/2)^2-x

Algebra ->  Exponents -> SOLUTION: Without using a calculator, solve for x: a) 8^x = 1/ sqrt( 2 ) b) 4^2x+1 = (1/2)^2-x      Log On


   

Question 701470: Without using a calculator, solve for x:
a) 8^x = 1/ sqrt( 2 )
b) 4^2x+1 = (1/2)^2-x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Without using a calculator, solve for x:
a) 8%5Ex+=+1%2Fsqrt%282%29
Write the square root as an exponent
8%5Ex+=+1%2F2%5E%281%2F2%29
CAn also be written
8%5Ex+=+2%5E%28-1%2F2%29
8 can be written as 2^3
2%5E%283x%29+=+2%5E%28-1%2F2%29
therefore
3x = -1%2F2
x = -1%2F2*1%2F3
x = -1%2F6

b) 4%5E%28%282x%2B1%29%29+=+%281%2F2%29%5E%28%282-x%29%29
we can rewrite this to
2%5E%282%282x%2B1%29%29+=+2%5E%28-%282-x%29%29
2%5E%28%284x%2B2%29%29+=+2%5E%28%28x-2%29%29
therefore
4x + 2 = x - 2
4x - x = -2 - 2
3x = -4
x = -4%2F3