SOLUTION: Solve: 16^2x+1=8^x

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve: 16^2x+1=8^x      Log On


   

Question 121325: Solve: 16^2x+1=8^x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Does the problem look like this: 16%5E%282x%2B1%29=8%5Ex?

16%5E%282x%2B1%29=8%5Ex Start with the given equation



%282%5E4%29%5E%282x%2B1%29=%282%5E3%29%5Ex Rewrite 16 as 2%5E4 and rewrite 8 as 2%5E3



2%5E%284%282x%2B1%29%29=2%5E%283x%29 Multiply the exponents



4%282x%2B1%29=3x Since the bases are equal, the exponents are equal. So set the exponents equal to each other and solve.




8x%2B4=3x Distribute


8x=3x-4Subtract 4 from both sides


8x-3x=-4 Subtract 3x from both sides


5x=-4 Combine like terms on the left side


x=%28-4%29%2F%285%29 Divide both sides by 5 to isolate x



x=-4%2F5 Reduce

--------------------------------------------------------------
Answer:
So our answer is x=-4%2F5 (which is approximately x=-0.8 in decimal form)