SOLUTION: Determine x for 10^2x + 1 = 1000^x - 1 a. x = -2 b. x = 4 c. x = 9 d. No solution

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Determine x for 10^2x + 1 = 1000^x - 1 a. x = -2 b. x = 4 c. x = 9 d. No solution       Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 148215: Determine x for 10^2x + 1 = 1000^x - 1
a. x = -2
b. x = 4
c. x = 9
d. No solution

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
10%5E%282x+%2B+1%29+=+1000%5E%28x+-+1%29 Start with the given equation.


10%5E%282x+%2B+1%29+=+%2810%5E3%29%5E%28x+-+1%29 Rewrite 1000 as 10%5E3


10%5E%282x+%2B+1%29+=+10%5E%283%28x+-+1%29%29 Multiply the exponents.


10%5E%282x+%2B+1%29+=+10%5E%283x+-+3%29 Distribute.


2x%2B1=3x-3 Since the bases are equal, this means that the exponents are equal.


2x=3x-3-1 Subtract 1 from both sides.


2x-3x=-3-1 Subtract 3x from both sides.


-x=-3-1 Combine like terms on the left side.


-x=-4 Combine like terms on the right side.


x=%28-4%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=4 Reduce.


----------------------------------------------------------------------

Answer:

So the answer is x=4