log with base 2(x^2-2x+5)=2 solve the equation. (The base 2 is the little 2 bottom right of log)

Question

log with base 2(x^2-2x+5)=2    solve the equation. (The base 2 is the little 2 bottom right of log)

dumbcow · Answer

rewrite in exponential form
$$x^{2}-2x+5 = 2^{2}$$

anonymous · Answer

nvm i think the answer is 1...

dumbcow · Answer

yep :)

anonymous · Answer

=]

anonymous · Answer

actually how do I work out the problem? I used a calculator, lol

anonymous · Answer

quadratic equation, or factoring, gives you 1.

anonymous · Answer

log(x^2-2x+5)/log(2)=2  is all i have

anonymous · Answer

what do i do from there?

anonymous · Answer

i think you did your change of base formula wrong the log(2) in the denominator should be log base 2 and the log in the numerator should be log base 10. However that is the hard way.

anonymous · Answer

look at the first post by dumb cow

anonymous · Answer

i just figured it out with quadratic equation :P I forgot to minus 4 on each side.

anonymous · Answer

well i meant factoring.

anonymous · Answer

$$\log_{2}(x^2-2x+5)=2 $$

from here you raise both sides by the base

$$2^{\log_{2}(x^2-2x+5)} = 2^{2} $$

this erase the log and the equation can be simplified to 

$$x^2-2x+5=2^2$$