Question

The value of x that satisfies the equation log x + log (x - 7)

Answer 1

log(X-7)+log(X)= log(2)+log(X+11)
Subtract log(2)+log(X+11) from both sides:
-log(2)+log(X-7)+log(X)-log(X+11) = 0 We can rewrite the left side:
log(1/2)+log(X-7)+log(X)+log(1/(X+11))= 0 Simplify:
log((X (X-7))/(2 (X+11)))= 0
Cancel logarithms by taking exp of both sides:
(X(X-7))/(2(X+11))= 1
Multiply both sides by 2(X+11):
X(X-7)= 2(X+11)
Expand out terms of the left:
X^2-7X = 2(X+11)
Expand out terms of the right:
X^2-7X = 2X+22
Subtract 2X+22 from both sides:
X^2-9X-22 = 0
Factor the left:
(X-11) (X+2) = 0
Split into two equations:
X-11= 0 or X+2= 0
X= 11 or X= -2
by putting these two values in the equation
you will get that
x=11