Question

I need to solve for x

Answer 1

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