Question

Order the steps to solve the equation

log(x2 - 15) = log(2x) form 1 to 5.
x² - 2x - 15=0
Potential solutions are -3 and 5
IIIII
x² - 15 = 2x
x - 5 = 0 or x + 3 = 0
(x - 5)(x + 3) = 0

Answer 1

Attention for the conditions:

`x^(2) -15>0\\2x>0\\so\\x>0`

Explanation:

we have

`log(x^(2)-15)= log(2x)\\\\x^(2) -15 = 2x\\\\x^(2) -5x+ 3x-15=0\\ (x^(2)-5x)+(3x-15)=0\\ x(x-5)+3(x-5)=0\\(x-5)(x+3)=0\\x-5=0, x=5 \\\\x+3=0, x= -3`

So the solutions are 5 because x>0