You can
put this solution on YOUR website!Here's another hint: we can rewrite
as
and
. In other words,
So
transforms into
. Now do you see how the substitution
will help?
If not, then just repost or ask me.
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New stuff....
Start with the given equation.
Rewrite
as
(see above).
Now let
Replace each
with 'u'
Take note that we now have a much simpler quadratic to solve.
Notice that the quadratic
is in the form of
where
,
, and
Let's use the quadratic formula to solve for "u":
Start with the quadratic formula
Plug in
,
, and
Square
to get
.
Multiply
to get
Rewrite
as
Add
to
to get
Multiply
and
to get
.
Take the square root of
to get
.
or
Break up the expression.
or
Combine like terms.
or
Simplify.
So the solutions (in terms of 'u') are
or
However, we want the solutions in terms of 'x'.
Let's find the solution of 'x' that corresponds to
Go back to the substitution equation.
Plug in
Rewrite
as
. Note: ANY number (except 0) to the 0th power is 1.
Since the bases are equal, the exponents are equal. So
or
So the first solution is
-----------------------------------------
Let's find the solution of 'x' that corresponds to
Go back to the substitution equation.
Plug in
Take the log of both sides.
Since you CANNOT take the log of a negative number, this means that we cannot continue
So there isn't a corresponding solution of 'x' to
============================================================
Answer:
So the only solution is
Check:
Start with the given equation.
Plug in
Multiply
Raise 3 to the zeroth power to get 1.
Add
Subtract.
Since the equation is true, the solution
is verified.
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