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Problem #90
Problem #94
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90)
Start with the given equation
Let
. So this means that
(ie
)
Replace
with
and
with "z" (see above)
Notice we have a quadratic equation in the form of
where
,
, and
Let's use the quadratic formula to solve for z
Start with the quadratic formula
Plug in
,
, and
Negate
to get
.
Square
to get
.
Multiply
to get
Subtract
from
to get
Multiply
and
to get
.
Take the square root of
to get
.
or
Break up the expression.
or
Combine like terms.
or
Simplify.
Now remember, we let
. So this means that
or
Start with the first equation
Take the log base 3 of both sides (to isolate "x")
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Move onto the second equation
Take the log base 3 of both sides (to isolate "x")
Evaluate the log base 3 of 3 to get 1
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Answer:
So the solutions are
or
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94)
Is the equation
????
If so, then....
Start with the given equation
Let
and
So the equation then becomes...
Now let's evaluate the individual pieces:
Start with the first assignment
Use the change of base formula to break up the log
Rewrite 125 as
. Note:
Pull the exponent down and place it out front.
Divide and cancel out the common terms.
Since
, this means that
(this is the first piece)
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Now move onto the second assignment
Use the change of base formula to break up the log
Rewrite 125 as
. Note:
Pull down the exponent.
Divide and cancel out the common terms.
Since
, this means that
(which is the second piece)
Go back to the original equation
Plug in
and
Distribute the exponent.
Cube 1 to get 1. Cube 3 to get 27.
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Answer:
So the answer is
This means that
(