If a, b are the solutions of the equation
log base of 2(5 − 2x) + log base of 2(5 + 2x) = 2 ,
find the value of the product ab. I know the law is log base 2 (5-2x)(5+2x)=2 So After I foil, I get 25+10x-10x-4x^2. I then set -4x^2+25=2 and solve for x. I pretty much get x=square root of 23/4 however that is not an answer choice. Did I do something wrong?

Question

If a, b are the solutions of the equation
log base of 2(5 − 2x) + log base of 2(5 + 2x) = 2 ,
find the value of the product ab.      I know the law is log base 2 (5-2x)(5+2x)=2 So After I foil, I get 25+10x-10x-4x^2. I then set -4x^2+25=2 and solve for x. I pretty much get x=square root of 23/4 however that is not an answer choice. Did I do something wrong?

campbell_st · Answer

well what you forgot was to raise the right hand side of the equation as a power of 2


so it should be -4x + 25 = 2^2

                        -4x + 25 = 4


now solve for x

anonymous · Answer

Thank you so much @campbell_st

campbell_st · Answer

hope it helps... remember for equations its the same thing on both sides of the =