SOLUTION: 4^(x+1)= (1/8)^(x+6)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 4^(x+1)= (1/8)^(x+6)      Log On


   

Question 975484: 4^(x+1)= (1/8)^(x+6)
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%28x%2B1%29=+%281%2F8%29%5E%28x%2B6%29

Replace 4 by 2² and 8 by 2³ 

%282%5E2%29%5E%28x%2B1%29=+%281%2F2%5E3%29%5E%28x%2B6%29

Remove parentheses by distributing (multiplying) exponents:

2%5E%282x%2B2%29+=+1%5E%28x%2B6%29%2F2%5E%283x%2B18%29

2%5E%282x%2B2%29+=+1%2F2%5E%283x%2B18%29

Multiply both sides by 2%5E%283x%2B18%29

2%5E%282x%2B2%29%2A2%5E%283x%2B18%29+=+1

Add exponents of 2

2%5E%285x%2B20%29=1

Since we know that 2%5E0=1,

5x+20 = 0
   5x = -20
    x = -4

Edwin

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
4^(x+1)= (1/8)^(x+6)
4%5E%28x+%2B+1%29+=+%281%2F8%29%5E%28x+%2B+6%29

%282%5E2%29%5E%28x+%2B+1%29+=+%282%5E%28-3%29%29%5E%28x+%2B+6%29 ------ Replacing 4 with 2%5E2, and 1%2F8 with 2%5E%28-+3%29

2%5E%282x+%2B+2%29+=+2%5E%28-+3x+-+18%29

2x + 2 = - 3x – 18 ------- Since bases are equal, their exponents are too

2x + 3x = - 18 – 2

5x = - 20

x = %28-+20%29%2F5, or highlight_green%28x+=+-+4%29