Logarithmic equation.. need help finding the answer! please help it's an emergency! :)?

Question

Ok. Solve the logarithmic equation. round answer to 3 decimal places, if necessary.

1. log(x+1) + log(x-2) = log4

2. log(base of 5) (x+4) + log(base of 5) x = 1

I know the addition means multiplication, right? well I can't seem to factor it out right. But this is going to be graded and I really need to get a 100! So please help me, or atleast help me solve the equation to get the answer!

The first one my answer is 141.42, i really think i am major wrong with that one lol

And for the second one i got - 4

Thanks!

at least 1 answer! :)

do both of the 2 answers for each equation check right with the equation? or do you throw one of them out?

i have in my notes that the answer has to be positive and if it is not throw it out. am i reading my notes right?

Answer 1

Question 1
log (x + 1)(x - 2) = log 4
(x + 1)(x - 2) = 4
x² - x - 2 = 4
x² - x - 6 = 0
(x - 3) (x + 2) = 0
x = 3 (+ ve value for x)

Question 2
log (x + 4)(x) = 1
(x + 4) (x) = 5^1
x² + 4x - 5 = 0
(x + 5)(x - 1) = 0
x = 1 (+ ve value for x)

Answer 2

1..log(x+1) + log(x-2) = log4
log(x^2-x-2)=log 4
x^2-x-2=4
x^2-x-6=0
(x-3)(+2)=0
x-3=0 or x+2=0
x=3 or x=2

2. log(base of 5) (x+4) + log(base of 5) x = 1
log(base of 5) (x^2+4x)=1
x^2+4x=5
x^2+4x-5=0
(x-1)(x+5)=0
x-1=0 or x+5=0
x=1 or x=-5

remember that log a +log b =log (ab)

Answer 3

1. log (x+1)*(x-2) = log 4
(x+1)(x-2) = 4
x^2 - x - 2 = 4
x^2 - x -6 = 0
(x-3)(x+2) = 0
x = -2,3
2. log(base 5) (x+4)x = 1
5 = x^2 + 4x
x^2 +4x -5 = 0
(x+5)(x-1) = 0
x = -5,1

Answer 4

a million). Ln(x+2) - Ln(x) = 4 Ln(x+2/x) = 4 Ln A - Ln B = Ln(A/B) taking e on the two sides (x+2)/x = e^4 x+2 = xe^4 xe^4-x = 2 x(e^4-a million) = 2 x = 2/ (e^4-a million) 2). 2Ln(x-3) = Ln(7x) Ln(x-3)^2 = Ln(7x) (x-3)^2 = 7x x^2-6x+9 = 7x x^2-6x-7x+9 = 0 x^2-13x+9 = 0 so x = {13 + sq. root(13^2-4*a million*9)}/2 and {13 - sq. root(13^2-4*a million*9)}/2 = {13+ sqrt(133) } / 2 and {13- sqrt(133) } / 2