Solve for X.?

Question

log3 (x+3) + log3 (x+5) =1

Answer 1

log(x+3)(x+5) base 3=1
(x+3)(x+5)=3
x^2+8x+15=3
x^2+8x+12=0
(x+6)(x+2)=0
x=-2 or -6

Answer 2

log3 (x+3)(x+5) = 1
(x+3)(x+5) = 3^1
x² + 8x + 15 = 3
x² + 8x + 12 = 0
(x + 2)(x + 6) = 0
x = -2 or x = -6

But -6 would cause a problem in the original equation, so x=-2.

Everyone seems to forget that you have to make sure that the equation still works by plugging the values back in.

You can't take the ln of a negative number, so any value of x that results in taking the ln of a negative number has to be thrown out.

Answer 3

Log3 ((x+3)(x+5))=1
log3 ( x^2+8x+15)=1

3^1=x^2+8x+15
x^2+8x+12=0
(x+2)(x+6)=0
x=-2,-6

Answer 4

One property of logarithms is log(y)+log(x) =log(x*y).

So log3(x+3)+log3(x+5)=log3((x+3)*(x+5))=log3(x^2+8x+15)
So log3(x^2+8x+15)=1. Exponentiate both sides by three. Then
3^(log3(x^2+8x+15))=3^1
so
(x^2+8x+15)=3
x^2+8x+12=0
This is a quadratic equation and you can find the roots using the formula. r=(-b±sqrt(b^2-4ac))/(2a)

Answer 5

log3 (x) + log 3(3) + log3 (x) + log 3(5)=1

Take inverse log of both sides

3*10^x + 3*10^3+ 3*10^x + 3*10^5= 10^1
3(10^x+10^x) + 3000+ 300000= 10
20^x= 100996
ln (20^x)= ln 100996
x ln 20= 11.52
x= 11.52/ (ln20)
x=3.84

Answer 6

im solving it now...have to look at you own formulae to understand...

log3(x+3) + log3(x+5)=1
log(x+3)/log3 + log(x+5)/log3=log0............since log0=1
log(3+3-3) + log(x+5-3) = log0
logx + log(x+2) = log0
log(x*(x+2))=log0
x*x + 2*x = 0...............taking antilog on both sides
x=-2


so, IMO, x= -2


To avoid confusions in quadratic equations when you have to check if you're still getting the answer, simply try to remove/avoid it, by adopting the above method.

Answer 7

log(x+3)(x+5) base 3=1
(x+3)(x+5)=3
x^2+8x+15=3
x^2+8x+12=0
(x+6)(x+2)=0
x=-2 or -6

Answer 8

if the base is 3 then
x^2+8x+12=0
find the roots.

Answer 9

-3 and -6
i tink