SOLUTION: 90) 3^2x -8 . 3^x +15=0 94) If x= (log125 5)^log5 125 Please help me to solve this two. Thank You

Question 170138This question is from textbook intermediate algebra
: 90) 3^2x -8 . 3^x +15=0
94) If x= (log125 5)^log5 125
Please help me to solve this two. Thank You
This question is from textbook intermediate algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Table of Contents:
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
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