SOLUTION: Hi guys, im stumped with this one: 2ln2 - ln(x-1) = ln(2x) solve for 'x'. cheers =)

Question 186597: Hi guys, im stumped with this one:
2ln2 - ln(x-1) = ln(2x)
solve for 'x'.
cheers =)
Found 2 solutions by nerdybill, josmiceli:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
You will need to apply "log rules".
Review them at:
http://www.purplemath.com/modules/logrules.htm
.
2ln2 - ln(x-1) = ln(2x)
2ln(2/(x-1)) = ln(2x)
ln(2/(x-1))^2 = ln(2x)
(2/(x-1))^2 = 2x
2^2/(x-1)^2 = 2x
4/(x-1)^2 = 2x
2/(x-1)^2 = x
2 = x(x-1)^2
2 = x(x-1)(x-1)
2 = x(x^2-x-x+1)
2 = x(x^2-2x+1)
2 = x^3-2x^2+x
0 = x^3-2x^2+x-2
Factor (by grouping) on the right:
0 = (x^3-2x^2)+(x-2)
0 = x^2(x-2)+(x-2)
0 = (x-2)(x^2+1)
.
Setting each term (in parenthesis to zero) we get:
x = {2, i}

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
In general:

and

check:

OK

The negative root doesn't work since
raising to a power can't
result in a negative

RELATED QUESTIONS
Hi guys i need some help with this question. expand the quantity as sum and... (answered by ankor@dixie-net.com)
SOLVE FOR X ln(ln x) =... (answered by vleith)
Solve... (answered by stanbon)
Solve for x: ln (2x-1) = ln 5 - ln... (answered by josgarithmetic,amarjeeth123)
Hi guys i need some help with this question. Please help me solve this equation:... (answered by flame8855)
Solve: log base 4 (X) + Log base 8 (x) = 1 ln X/ln 4 + ln X/ln 8=1 2 ln X/2 ln 4 + ln... (answered by Fombitz)
Solve for x:... (answered by stanbon)
Solve the following equation for x. I've been trying this one and have had difficulty. (answered by Fombitz)
-could you please help me in this problem solve for x: ln(x-1)=ln(x-2)-ln... (answered by josgarithmetic)