solve the following equation.
log 1/6 (x^2+x)- log 1/6 (x^2-x)=2
**the 1/6 is lowered on both sides and the (x^2+x) and (x^2-x) should be higher on both sides**
take a look at the post by Krystal (unless you are that same person, the posting looks very similar)
http://www.jiskha.com/display.cgi?id=1357052002
all you have to change is the base from 1/3 to 1/6
I think you can handle the rest.
(x^2+x)/(x^2-x) = (1/6)^2
(x+1)/(x-1) = 1/36
36x+36 = x-1
35x = -37
x = -37/35
Thanks Steve. I don't know why but when I see (1/6)^2 for some reason I want to just multiply the 6*2. It for some reason doesn't seem to stick that it is 6*6 to equal 36. I worked the problem--just had different numbers since I multiplied 6*2 to get 12.
To solve the equation:
1. Start by using the logarithmic properties to simplify the equation. Recall that log(a) - log(b) = log(a/b).
log(1/6)(x^2 + x) - log(1/6)(x^2 - x) = 2
log(1/6)((x^2 + x)/(x^2 - x)) = 2
2. Apply the property log(base a)(x/y) = log(base a)x - log(base a)y to separate the logarithms.
log(1/6)(x^2 + x)/(x^2 - x) = 2
3. Rewrite the equation using the exponential form of logarithms. Recall that log(base a)a^b = b.
(1/6)^2 = (x^2 + x)/(x^2 - x)
4. Simplify the expression, remembering that (1/6)^2 = 1/36.
1/36 = (x^2 + x)/(x^2 - x)
5. Multiply both sides of the equation by (x^2 - x) to eliminate the denominator.
(x^2 - x) * (1/36) = x^2 + x
6. Expand and simplify the equation.
x^2 - x = 36(x^2 + x)
7. Distribute 36 to both terms on the right side.
x^2 - x = 36x^2 + 36x
8. Move all the terms to one side of the equation to set it to zero.
0 = 36x^2 + 36x - x^2 + x
0 = 35x^2 + 37x
9. Factor out common terms, if possible.
0 = x(35x + 37)
10. Set each factor equal to zero and solve for x.
x = 0 or 35x + 37 = 0
11. Solve the second equation.
35x + 37 = 0
35x = -37
x = -37/35
12. The solutions to the equation are x = 0 and x = -37/35.