Asked by jh
For the following, use the inverse relationship between logarithms and exponentials to determine x.
log2(x^2−2x)=3
Solution Set:_____________?
I don't know how to do this question at all :( Please help and show the work as well so that I can learn! Thanks.
log2(x^2−2x)=3
Solution Set:_____________?
I don't know how to do this question at all :( Please help and show the work as well so that I can learn! Thanks.
Answers
Answered by
Reiny
log2(x^2−2x)=3
by definition
x^2 - 2x = 2^3
x^2 - 2x - 8 = 0
(x-4)(x+2) = 0
x = 4 or x + -2
testing:
if x=4
log<sub>2</sub> (16 -16) = 3
log<sub>2</sub> 0 = 3 , which is not true since log 0 is undefined
if x = -2
log<sub>2</sub> (4 + 4) = 3
log<sub>2</sub> (8) = 3 , which is true
so x = -2
by definition
x^2 - 2x = 2^3
x^2 - 2x - 8 = 0
(x-4)(x+2) = 0
x = 4 or x + -2
testing:
if x=4
log<sub>2</sub> (16 -16) = 3
log<sub>2</sub> 0 = 3 , which is not true since log 0 is undefined
if x = -2
log<sub>2</sub> (4 + 4) = 3
log<sub>2</sub> (8) = 3 , which is true
so x = -2