SOLUTION: Can you please show me how to do the following problem: Find all real solutions to the equations a) ln^2x-5ln^x=-6 and b) 2 * ln(x)= ln(36)

Question 316702: Can you please show me how to do the following problem: Find all real solutions to the equations a) ln^2x-5ln^x=-6
and
b) 2 * ln(x)= ln(36)
thank you!!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
We're going to use the following identities/properties:

1)

2)

3) If , then

a)

Start with the given equation.

Use identity #1

Use identity #2

Convert the equation into exponential form.

Rewrite as

Reduce the expression on the left side.

Multiply both sides by .

Multiply both sides by .

Flip the equation.

Take the fourth root of both sides.

So the solution is

------------------------------------------------------------------
b)

Start with the given equation.

Use identity #1

Use property #3

Take the square root of both sides (note: we're ignoring the negative square root since you can't take the log of a negative number).

Take the square root of 36 to get 6.

So the answer is
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