4(100^(2x+1)) + 5 = 4005

Question

please show all steps used to solve for x. the answer is 0. Thanks

Answer 1

 4(100^(2x+1) + 5 = 4005

=> 4(100^(2x+1)   = 4005-5= 4000

=> 4(100^(2x+1)   = 4(1000)

 

Eliminate 4 from both side of the equation, you will get

 

100^(2x+1) = 1000 or 100^(3/2)  ( Remember 100^1/2 =10, 10^3=1000 )

 

Since both side of the equation has the same base of 100, now you can solve the power of the base directly.

 

Hence, we have 2x+1 = 3/2; by minus 1 from both sides we have 2x = 1/2, therefore, x = 1/4.

So Timothy T is correct!

 

 

 

 

 

 

Answer 2

Either you have the wrong answer or you have erroneously copied the problem.

 

If the problem was correctly copied, then the answer is x = 1/4 not x = 0.

 

 

Answer 3

1.  Subtract 5 from both sides.

2. Divide both sides by 4.

3. On the left side, express 100 as 10^2; on the right side express 1000 as 10^3.

4.  Equate the exponents for base 10, solve.