solve the equation for x. write the exact solution and the approximate solution to the nearest hundredth, when appropriate. ln(x-5)=ln(3x+1)

Question

anonymous · Answer

If you have written this problem correctly, you may want to go back and check.  There is no reall number value of x that will satisfy this equation.

anonymous · Answer

You could set it in your calculator as y1 = ln(x-5) and Y2 = (3x+1) and you will find that they don't equal the same x using real numbers. But algebraically you can solve it to get x=-3

zehanz · Answer

If ln(x-5)=ln(3x+1), then x-5=3x+1, which means: -5=2x+1 and so 2x=-6, or x=-3.
Seems OK, or?

Let's put it back into the original equation:

ln(-3-5) = ln(-8)
ln(3*-3+1)=ln(-8).

Although it looks ok, there is a problem: the ln-function cannot be calculated for negative numbers (or even 0)! So no real solutions exist.

anonymous · Answer

Took the words right outta my...ummm...fingers @ZeHanz

zehanz · Answer

It is important to check what kind of numbers are allowed beforehand, so as to avoid dissapointment :D

zehanz · Answer

@calmat01: sorry about that!

anonymous · Answer

lol...np!

anonymous · Answer

thank you everyone!
@ZeHanz @TRowstudy @calmat01

zehanz · Answer

YW!