2007-05-10 01:59:55 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
log3(x+5) + log3(x-1) = 3
log3((x+5)(x-1)) = 3
(x+5)(x-1) = 27
x^2 + 4x - 5 = 27
x^2 + 4x - 32 = 0
(x + 8)(x - 4) = 0
x = -8 or x = 4
Now, clearly, x = -8 doesn't work in the original equation (would mean taking the log of a negative number), so x = 4 is our only solution.
2007-05-10 02:04:56 · answer #1 · answered by Tim M 4 · 0⤊ 0⤋
I assume log3 means log base 3. Note that in the below work, I take advantage of the fact that log(a) + log(b) = log(ab) as well as the fact that it is permissible to use both sides of an equation as the exponents of a common base. So in this case, I raised 3 to the power of each side in going from the third line to the fourth. Also note that 3^log3(n) = n by definition.
log3(x + 5) = 3 - log3(x - 1)
3 = log3(x + 5) + log3(x - 1)
3 = log3[(x + 5)(x - 1)]
27 = (x + 5)(x - 1)
27 = x^2 + 4x - 5
x^2 + 4x - 32 = 0
(x + 8)(x - 4) = 0
x + 8 = 0 or x - 4 = 0
x = -8 or 4
When we check these answers in the original question, we see that we must take the log3 of x + 5 and x - 1. With -8, these values are -3 and -9, which are negative numbers and we cannot take their log. With 4, the values are 9 and 3, which present no problem.
log3(9) = 3 - log3(3)
2 = 3 - 1
2 = 2
So the answer checks out.
2007-05-10 02:06:08 · answer #2 · answered by DavidK93 7 · 0⤊ 0⤋
Assume for ease of typing that log means log base 3
log (x + 5) + log (x - 1) = 3
log (x + 5).(x - 1) = 3
(x + 5).(x - 1) = 27
x² + 4x - 32 = 0
(x + 8).(x - 4) = 0
x = - 8, x = 4
Accept +ve value of x = 4
2007-05-10 02:47:17 · answer #3 · answered by Como 7 · 0⤊ 0⤋
log3(x+5) =3-log3(x-1)
log3(x+5) =log1000-log3(x-1)
3(x+5=1000/3(x-1)
9(x^2+4x-5)=1000
9x^2+36x-45-1000=0
9x^2+36x-1045=0
x=19,-55answer
2007-05-10 02:14:13 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Taking your question at face value and that you are working in base 10
log(3x + 15) = 3 - log(3x - 3)
log(3x + 15) + log(3x - 3) = 3
log(3x + 15)(3x - 3) = 3
(3x + 15)(3x - 3) = 10³
9x² + 36x - 45 = 1000
9x² + 36x - 955 = 0
and use the quadratic formula since it doesn't factorise
2007-05-10 02:32:29 · answer #5 · answered by fred 5 · 0⤊ 0⤋
your equation no longer finished a. log 3x + 5 = 3 or b. log (3x+5) = 3? a) log 3x + 5 = 3 log 3x = 3-5 log 3x = -2 3x = 10"(-2) 3x = 0.01 x= 0,00333 b) log (3x + 5) = 3 3x + 5 = 10"3 3x = one thousand-5 3x = 995 x = 331,667 ok, desire solved.
2016-11-26 23:51:21 · answer #6 · answered by caren 4 · 0⤊ 0⤋
The answer is "Mule Terds"... Am I right?
2007-05-10 02:02:39 · answer #7 · answered by Big Man Shrinking 1 · 0⤊ 2⤋