SOLUTION: Solve: log(x-3) + log(x+5) =1 My teacher said to use the log of products to get an equivalent quadratic equation. I don't really follow him on how to do it, though.

Question 299113: Solve: log(x-3) + log(x+5) =1
My teacher said to use the log of products to get an equivalent quadratic equation. I don't really follow him on how to do it, though.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
What he means is to apply a "log rule":
log a + log b = log (ab)
.
Solve: log(x-3) + log(x+5) =1
log(x-3)(x+5) =1
(x-3)(x+5) =10^1
x^2+5x-3x-15 = 10
x^2+2x-15 = 10
x^2+2x-25 = 0
Solve by applying the quadratic formula. Doing so yields:
x = {4.1, -6.1}
Plug the above back into the original equation to check whether they are viable answers. The negative answer will not work (it's an extraneous solution) throw it out leaving:
x = 4.1
.
Details of quadratic formula to follow:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=104 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4.09901951359278, -6.09901951359278. Here's your graph:

RELATED QUESTIONS
Rewrite each as an equivalent exponential equation. 1) log(3)5=y 2 log(a)7=-2... (answered by ankor@dixie-net.com)

This equation is on a work sheet that I need to solve: log (X+5) - log (X-1) = log... (answered by Earlsdon)

Hi. I'm am required to find x in this equation: {{{log (5, (5-4x))}}} = {{{log (sqrt(5),... (answered by Earlsdon)

Help! Use the rules of logarithms to show that the following are equivalent. log 144... (answered by mukhopadhyay)

How would you solve log base 6 of 2x + log base 6 of (x-2) = 1? Our teacher said the... (answered by Alan3354)

log(x)- log(x-1)=1/2 The teacher says to solve for t in this one too but I see no t... (answered by lwsshak3)

Help on this one....what am I to solve to get the answer? Solve the equation(not in... (answered by bucky)

log base 3 of (5x-10)-log base 3 of 12=1 i have to solve the equation for... (answered by Fombitz)

how is 1-3 log base 5 of x equivalent to log base 5... (answered by stanbon)