# Homework Help: Logarithms question

1. Oct 21, 2011

### Doubell

1. The problem statement, all variables and given/known data
NEED HELP WITH THIS MATH PROBLEM: LOG3(X+3) + LOG3(X-1) = 1

2. Relevant equations

3. The attempt at a solution
I SAID LOG3(X+3) + LOG3 (X-1)
SIMPLIFIES TO LOG3(X+3)*(X-1) = 1
I.E LOG3(X^2 +2X - 3) = 1
THEN 3^1 = (X^2 +2X - 3)
AND 0 = (X^2 +2X - 6)
THEN USE THE QUADRATIC FORMULA TO FIND X AS {-2+/- 28^1/2}/2
JUST NEED A SECOND OPINION TO SEE IF ITS CORRECT.

2. Oct 21, 2011

### ehild

The calculation is correct so far, but you have to investigate what root is solution of the original equation. Hint: is logarithm defined for negative numbers?

ehild

3. Oct 21, 2011

### Doubell

ok so logarithms are not defined by negative values hence the root for the original equation would have to be the positive value of x which would have been {-2 +[28^1/2]}/2 is that the final solution.

4. Oct 21, 2011

### ehild

Correct for the real logarithmic function.

(Later you will learn about complex numbers and functions, and the complex logarithm is defined for negative numbers, too. )

ehild