How do you solve this log equation???

Question

log3(x+1)+log3(x-7)=2

(3 is the base of the log)
HELP!!

Answer 1

log3(x+1)+log3(x-7)=2
log3+log(x+1)+log3+log(x-7)=2
1+log(x+1)(x-7)+1=2
or log(x+1)(x-7)=0
log(x+1)(x-7)=log1
or (x+1)(x-7)=1
now solve it by quadratic equation

Answer 2

log3(x+1)+log3(x-7)=2 =>
log3(x+1)(x-7)=log3 9 =>
(x+1)(x-7)=9 <=>
x^2 - 6x -16 = 0
Solving this quadratic eqn yields:
x=8
x=-2
Substituting these numbers into the initial eqn we find that the only solution is
x = 8

Answer 3

One of the log rules says : log(A) + log(B) = log(A*B).

Therefore, log[3](x + 1) + log[3](x - 7) = log[3](x + 1)(x - 7)

Now we have : log[3](x + 1)(x - 7) = 2

Another rule says if log[b](N) = P, then N = b^P.

Therefore, (x + 1)(x - 7) = 3^2

or, x^2 - 6x - 7 = 9
or, x^2 - 6x - 16 = 0
or, (x + 2)(x - 8) = 0
or, x = -2 or 8

If x = -2, then x + 1 = -1 and x - 7 = -9,
but you can't take the log of a negative number.
Therefore, x = -2 is not a solution.

So the only solution is x = 8.

Answer 4

log3(x+1) + log3(x-7) = 2
log3[(x+1)(x-7)] = 2
3^2 = (x+1)(x-7)
x^2 - 6x - 7 = 9
x^2 - 6x -16 = 0
(x-8)(x+2) = 0

X = 8, -2

-2 is not a solution. Or else, both logarithms will be undefined.


SS = {8}

Answer 5

log_3(x + 1) + log_3(x - 7) = 2

The sum of logs is equal to the log of the products of the arguments.

log_3((x + 1)(x - 7)) = 2

I'm going to raise 3 to the power of each side of the equation.

(x + 1)(x - 7) = 9
x^2 - 6x - 7 = 9
x^2 - 6x - 16 = 0
(x - 8)(x + 2) = 0
x = 8 or -2

In a log equation, it's very important to check all of the initial answers to verify that you haven't got any undefined results.

log_3(8 + 1) + log_3(8 - 7) = log_3(9) + log_3(1) = 2 + 0 = 2 ==> correct
log_3(-2 + 1) + log_3(-2 - 7) = log_3(-1) + log_3(-9), and logs of negative numbers are undefined.

x = 8 is the only answer.

Answer 6

log(X+1) + log(X-7) + 2
recall that log(a*b) = log(a) + log(b), so....
log(2X-6) = 2
now express an the "antilogs"
3^(2X-6) = 3^2
(3^2X) * (3^-6) +3^2
now divide both sides by 3^-6
3^2X = 3^8
2X = 8
X = 4

Answer 7

(3x+3)+(3x-21)=2
so 6x+24=2
6x=2-24=-22
x=-22/6
I cant do the rest properly so its gonna be guesswork(sorry :()
Answers gonna be around -4