SOLUTION: solve for x. 2^(x^2-x+10)=16^(7-x) if there is more than one solution, separate them with commas.

Algebra ->  Equations -> SOLUTION: solve for x. 2^(x^2-x+10)=16^(7-x) if there is more than one solution, separate them with commas.      Log On


   

Question 964018: solve for x.
2^(x^2-x+10)=16^(7-x)
if there is more than one solution, separate them with commas.
Found 2 solutions by Murthy, MathTherapy:
Answer by Murthy(22) About Me  (Show Source):
You can put this solution on YOUR website!
2^(x^2-x+10)=16^(7-x)
Taking log with base 2 on both sides
(x^2-x+10)x log2(2)= (7-x)x log2(2^4)
=(x^2-x+10)x log(2)=(7-x)x 4xlog2(2)
cancel log2(2)on both sides
(x^2-x+10)=4(7-x)
x^2+3x-18=0
(x+6)(x-3)=0
therefore,
x=-6,3

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

solve for x.
2^(x^2-x+10)=16^(7-x)
if there is more than one solution, separate them with commas.
highlight%282%5E%28x%5E2+-+x+%2B+10%29+=+16%5E%287+-+x%29%29

2%5E%28x%5E2+-+x+%2B+10%29+=+%282%5E4%29%5E%287+-+x%29%29

2%5E%28x%5E2+-+x+%2B+10%29+=+2%5E%284%287+-+x%29%29

x%5E2+-+x+%2B+10+=+4%287+-+x%29 --------- Bases are equal and so are their exponents 

x%5E2+-+x+%2B+10+=+28+-+4x

x%5E2+-+x+%2B+4x+%2B+10+-+28+=+0

x%5E2+%2B+3x+-+18+=+0

(x + 6)(x - 3) = 0

highlight_green%28x+=+-+6%29    	OR	highlight_green%28x+=+3%29