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# Solve for x: log3(x+5) =3-log3(x-1)?

### 7 Answers

- Tim MLv 41 decade agoFavorite Answer
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.

- DavidK93Lv 71 decade ago
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.

Source(s): http://en.wikipedia.org/wiki/Logarithm - ComoLv 71 decade ago
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

- Anonymous1 decade ago
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

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- fredLv 51 decade ago
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

- carenLv 44 years ago
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.