Expert: Sherman D. - 11/4/2004

Question
can we call the following equation  an exponential equation ?and how can we solve it ?
(x-1)^(x-4)=(2x)^(x-4)

Answer
if something is in a form of y = ab^x form, its an exponential equation, on one condition, as long as "b" is positive.

just think of your problem as

y = (x - 1)^(x - 4)
a = 1
b = 2x
x = (x - 4)

anyway

(x - 1)^(x - 4) = (2x)^(x - 4)

since both (x - 1) and (2x) have the same exponent, which is (x - 4), you can think of your problem like this instead

x - 1 = 2x
-x = 1
x = -1

another way, you can mathematically solve it like this

(x - 1)^(x - 4) = (2x)^(x - 4)

(x - 4)root both sides

(x - 4)rt((x - 1)^(x - 4)) = 2x

the (x - 4)rt and ^(x - 4) cancel out, leaving you with

x - 1 = 2x

add 1 and subtract 2x from both sides and you get

-x = 1

divide both sides by -1

x = -1

If you have anymore, bring them on, i should be able to answer all of your questions that you may have pertaining to this type of problem, even others that may not have anything dealing with this. If you have any word problems, there are some kinds i can't answer, but if you think i can, then just send them to me. Also i don't do probability problems.

sorry about not catching the x = 4 part.