I am stuck on another logarithmic equation:
log3 x - 2 = log3 (x - 8)
Now, I assume log3 cancels out, which leaves:
x - 2 = x - 8
But from there, I am unsure how you would get x by itself, because if you try and transfer x to just one side, it cancels out because you have x and -x. I think I am on the wrong track though, so all guidance will be much appreciated once again.
If the problem was, indeed, , then what you did is exactly correct- ln(x) is a "one-to-one function" so it must be true that x- 2= x- 8. But no matter what x is, that is the same as -2= -8 which is not true. NO value of x makes that equation true.
But,as mr fantastic said, your lack of parentheses makes this problem ambiguous. It might be , , , or . The first and last of those, which would be the most reasonable interpretations, have no solution!
Thanks for the help Mr Fantastic and HallsofIvy. I have solved for x and checked my answer and the equation is indeed of the form: log3 (x) -2 = logx (x - 8).
So, what I did was:
log3(x) = logx (x - 8) + 2
Then I moved the logx(x - 8) to the other side by dividing both sides. So I get:
log3(x / x - 8) = 2
This turns into:
log3( x / x - 8) = (3 to the power of 2)
Then I multiplied the x - 8 back over:
log3(x) = 9(x - 8)
log3(x) = 9x - 72
Multiply the x over as well:
0 = 8x - 72
Move the 72 to the other side
8x = 72
Divide by 8 to yield:
x = 9.
Cool! Many thanks for the help!