need help with homework problem, due tuesday 08/09/2005

Use the log rules you've learned to combine the two logs on the right-hand side. This will give you "log(something) equals log(something else)". Equate "something" to "something else", and solve the resulting rational equation.

Eliz.
 
so would it be

log(x+1)=log((x+5)(x-2))

which would allow the logs to cancel

(x-1)= (x+2)(x-5)

is that right, because my teacher did not throughly explain these laws and how to apply them.
 
One rule says that addition outside logs becomes multiplication inside logs. But what is the rule for subtraction?

Eliz.
 
the division doesn't work you end up getting -3 + or - the square root of 21. it makes the logs negative and that doesn't exist.
 
Please reply showing all of your steps, so we can see how you got your solution. Thank you.

Eliz.
 
with the division i got

(x-1)= (x-2)/ (x+5)

multiply both sides by (x+5)

(x-1)(x+5)= (x-2)

x^2+4x-5= x-2

x^2 +3x-3=0

then i used the quadratic formula

-3 + or - the square root of 3^2 - 4(1)(-3)/ 2(1)

-3 + or - the square root of 21.

x= 1.582 and x= -7.582
 
Your work is correct. Obviously, the negative solution won't work in the original equation, so toss that. This leaves you with "x = [-3 + sqrt(21)]/2". Check this:

. . . . .x - 1: [-3 + sqrt(21)] / 2 - 1 = [-5 + sqrt(21)] / 2

. . . . .x - 2: [-3 + sqrt(21)] / 2 - 2 = [-7 + sqrt(21)] / 2

. . . . .x + 5: [-3 + sqrt(21)] / 2 + 5 = [7 + sqrt(21)] / 2

. . . . .(x - 2) / (x + 5): [-7 + sqrt(21)] / [7 + sqrt(21)]

Rationalizing this last, we get:

. . . . .[-49 + 14sqrt(21) - 21] / [49 - 21] = [14sqrt(21) - 70] / [28] = [sqrt(21) - 5] / 2

This is the same as the value of the left-hand side's argument, so the solution is valid.

(Note: Solutions are not required to be nice and neat. Don't be scared off just because a solution is messy. You could still be correct.)

Eliz.
 
i still do not understand how you got the solutions for

(x-1)
(x-2)
(x+5)

i know that you pluged in the values for x= -3 + the sqaure root of 21/2.
but i still get a negative number when i do this

log {(-3+square root of 21)/2} -1= log {(-3+ square root of 21)/2} -2 - log {(-3+ square root of 21)/2} +5
 
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