Answer:
x=2+√14
Step-by-step explanation:
log(x)+log(x−4)=1
log(x to the second power−4x)=1
Step 1: Solve Logarithm.
log(x2−4x)=1
10log(x2−4x)=101(Take exponent of both sides)
x2−4x=101
x2−4x=10
x2−4x−10=10−10(Subtract 10 from both sides)
x2−4x−10=0
For this equation: a=1, b=-4, c=-10
1x2+−4x+−10=0
x=
−b±√b2−4ac
2a
(Use quadratic formula with a=1, b=-4, c=-10)
x=
−(−4)±√(−4)2−4(1)(−10)
2(1)
x=
4±√56
2
x=2+√14 or x=2−√14
Check answers. (Plug them in to make sure they work.)
x=2+√14(Works in original equation)
x=2−√14(Doesn't work in original equation)
Answer:
x=2+√14
